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

Follow 5
Answer

Please enter your answer

Gurukul Education Center

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

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

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

A refrigerator is marked for sale at Rs. 17600 inclusive of sales tax at the rate of 10%. Calculate the sales tax on the refrigerator?
Let the price of the refrigerator without sales tax = P. Here, the selling price S = 17600 and the rate of sales tax i.e., r = 10 S = P(1 + r/100) 1700= P(1 + 10/100) P * 11/10 = Rs. 17600 Therefore,...
Udaybhan
0 0
7
Define limit of the class and class interval?
Normally 1 hour per day, 3 Hour per day on Saturday and Sunday.
Mukesh

I want to take online classes on database/ ETL testing.

 

Also i look forward to teach Mathematics/Science for class X-XII
Both are co-related to each other but compare to DBA Jobs, ETL job is more demanding hence you take class for informatica tools and others.
Varsha
0 0
7
What is the formula for arithmetic mean for unclassified data?
Arithmetic mean of unclassified data x1, x2, x3, x4, ... xn = X X= x1+ x2 + x3 + x4+ ... + xn —--—--——--—--—--——--—--— . n
Raj
Mensuration
Mensuration is the basic maths which deals with the formulas of areas, volumes ,measurements
Anil

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

Ask a Question

Related Lessons

CBSE CLASS 10 IMPORTANT QUESTIONS VIDEO LINK
https://www.youtube.com/watch?v=qX4Ga6hrxJY

Swapna V.

0 0
0

Saurav

0 0
0
Class-10 L-4 Triangles Ex-6.1 Q2 (iii)

Ashish Bhatia

0 0
0
Mathematics average
Que : Average of 5 consecutive even numbers is 12 . Find the sum of 1st and last numbers. Sol : shortcut... If consecutive numbers average is given, then average is (1st + last)/2 = 12 Therefore sum of 1st and last = 12*2 = 24

Roshan Azeez

1 0
0
learning is fun ,,,teaching is just showing a student how to enjoy it .
teaching-finding effective ways to make learning fun for the child
G

G.haritha

0 0
0

Recommended Articles

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 >

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 >

Meet Sandhya R, a B.Sc tutor from Bangalore

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

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 >

Find Grade 10 Tuition near you
Grade 10 Tuition in Delhi
Grade 10 Tuition in Bangalore
Grade 10 Tuition in Hyderabad
Grade 10 Tuition in Kolkata
Grade 10 Tuition in Chennai
Grade 10 Tuition in Mumbai
Grade 10 Tuition in Pune
Grade 10 Tuition in Lucknow
Grade 10 Tuition in Noida
Grade 10 Tuition in Gurgaon
Online Tuition Class 10

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