Question

if m and n are odd positive integers then m square + n square is even but not divisible by 4 . justify

Answer 1

let's take the.m to be 3 and 5
3^2+5^2=9+25=34
so it is not divisible by 4 and it's even.
so it's proved..
I have checked already..about it so it's correct statement.can apply theorems

Answer 2

Step-by-step explanation:

Since m and n are odd positive integers, so let m = 2q + 1 and n = 2p + 1 ,

•°• m² + n² = ( 2q + 1 )² + ( 2p + 1 )² .

= 4( q² + p² ) + 4( q + p ) + 2 .

= 4{( q² + p² + q + p )} + 2 .

= 4y + 2 , where y = q² + p² + q + p is an integer .

•°• q² + p² is even and leaves remainder 2, when divided by 4 that is not divisible by 4.

Hence, it is solved

THANKS

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