UrbanPro

Location Set your Location

Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class 10 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 10 > Learn Mathematics > If m and n are odd positive integers, then m2 + n2...
✕

Search in

If m and n are odd positive integers, then m2 + n2 is even, but not divisible by 4. Justify.

Asked by Last Modified  

5 Answers

Learn Mathematics +1 Class IX-X Tuition

Follow 5
Answer

Please enter your answer

Maths Tutor

Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1 Hence x2 + y2 = (2k + 1)2 + (2p + 1)2 = 4k2 + 4k + 1 + 4p2 + 4p + 1 = 4k2 + 4p2 + 4k + 4p + 2 = 4(k2 + p2 + k + p) + 2 Clearly notice that the sum of square is even the number...
read more
Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1 Hence x2 + y2 = (2k + 1)2 + (2p + 1)2 = 4k2 + 4k + 1 + 4p2 + 4p + 1 = 4k2 + 4p2 + 4k + 4p + 2 = 4(k2 + p2 + k + p) + 2 Clearly notice that the sum of square is even the number is not divisible by 4 Hence if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4 cross check let m= 3 and n=5 3^2+5^2=34 34 is not divisible by 4 hence prove read less
Comments
Dislike Bookmark

Since m is odd m*m is also odd. This imply m*m+n*n is of the form 4*k+2 (Since m*m is of the form 4*k+1).
Comments
Dislike Bookmark

Since m is odd positive integer then we can write m=2a+1 and n=2b+1, such that a,b >0 m2+n2=(2a+1)^2+(2b+1)^2 = 4a^2+1+4a+4b^2+1+4b = 4a^2+4b^2+4a+4b+2 = 2(2a^2+2b^2+2a+2b+1) Above eqn is divisible by 2 but not divisible by 4.
Comments
Dislike Bookmark

Tutor

Let m=2a+1, n=2b+1 be two odd positive integers Now m^2+n^2=(2a+1)^2+(2b+1)^2 =4a^2+1+4a+4b^2+1+4b =4a^2+4b^2+4a+4b+2 =2(2a^2+2b^2+2a+2b+1) Therefore m^2+n^2 is divisible by 2 but not with 4 Example let m=1, n=5 m^2+n^2=(1×1)+(5×5)=1+25=26 26 is divisible by 2 but not with 4
Comments
Dislike Bookmark

Tutor

M=1,n=3 then m2+n2=one2+three2=10,10 is not divisible by 4
Comments
Dislike Bookmark

View 3 more Answers

Related Questions

Define pie chart and frequency polygon?
Pie chart: If you consider a circle and it into some several parts. for each part you allot some percentage of items okay.
Ambar
0 0
7
What is the complementary angles and supplementary angles?
Complementary angles are the angles which add up to 90° and supplementary angles are the angles that add up to 180°.
J.k.kavyadharshini
0 0
7
How do I get over 95% in the ICSE class 10 board exams?
U can get 95% marks if u work hard and study regularly 8to 10hours daily.u have also first go through the text book throghly and the do practice from different samples papers and 10years of previous years...
Tejas
0 0
5
What are the benefits of self-studying in class 9?
Self study is a must even if you attend coaching or take a tuition. It will help you understand, learn and reflect effeciently.
Nazia
0 0
8
Is it necessary to pay for computer tuition in class 10 ICSE?
YES
Ushashree
0 0
5

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

practice 10 questions everyday to increase your speed,accuracy.
Practice 10 questions everyday to increase your speed in maths.Practice assignments during exams.
K

Kalyani

0 0
0
Tips To Score Excellent Marks In Maths
Hello students. Some tips for you all to score excellent marks in Maths: (1) Do not mug up sums and Theorems. Try to understand the concept. (2) Memorise all formulas and identities well. (3) Understand...

Deval T.

1 0
0
Find Cost Price ( x std Algebra) : Maharashtra board
Mahashtra Board X std Algebra (year 2020) A dealer sells a toy for Rs 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. Solution: SP selling price CP cost...

Venkatesan Iyer

0 0
0
Why am I learning Maths when I am not going to use it in everyday life?
A lot of students ask this question with a sense of boredom and servitude, "Why to study math if I can't use it ?". The answer to the question is pretty simple. You do use it in everyday life. Most of...

Sri Rama Chaitanya Kolluri

0 0
0
Euclid's divsion lemma application in finding H.C.F.
We know that Euclid's Division lemma states if a and b are two positive integers and a>b, then a=bq+r where q and r are two integers, where the value of r is given by 0<=r<b, This principle is...

Palak K.

0 1
0

Recommended Articles

Meet Mohammad Wazid, a skilled trainer for...

Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...

Read full article >

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Quest Academy - Institute of the month

Quest Academy is a professional Bangalore based NEET and JEE (Main + Advanced) training institute. The academy was incorporated in 2015 to cater to the needs of students, who aim to crack competitive exams by connecting with the best brains around. The institute helps students enhance their skills and capabilities through...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Find Class X Tuition near you
Class X Tuition in Delhi
Class X Tuition in Bangalore
Class X Tuition in Hyderabad
Class X Tuition in Kolkata
Class X Tuition in Mumbai
Class X Tuition in Chennai
Class X Tuition in Pune
Class X Tuition in Noida
Class X Tuition in Lucknow
Class X Tuition in Jaipur

Looking for Class 10 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 10 Tuition Classes?

The best tutors for Class 10 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 10 Tuition with the Best Tutors

The best Tutors for Class 10 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2024All Rights Reserved