Question

If m and n are odd positive integers, and m^square +n^square is even, but not divisible by 4. JUSTIFY. Its urgent.

Answer 1

Hey aditya

Here's your answer

We know that any positive odd integer is of the form 2q+1

Let m=2p+1

Let n=2q+1

So m²+n²=(2p+1)²+(2q+1)²

=4p²+4p+1+4q²+4q+1

=4p²+4q²+4p+4q+2

=4(p²+q²+p+q)+2

Let p²+q²+p+q=r

m²+n²=4r+2

So m²+n² is divisible by 2

Let us check whether m²+n² is divisible by 4 or not using Euclid's division lemma

a=bq+r

Let b=4

So the remainders can be 0,1,2,3

When r=2

a=4q+2

So any integer of the form 4q+2 isn't divisible by 4

So m²+n² isn't divisible by 4

Hope it helps!!