SOLUTION: Prove that if �a� and �b� are odd positive integers, then a2+b2 is even but not divisible by 4.

SOLUTION: Prove that if �a� and �b� are odd positive integers, then a2+b2 is even but not divisible by 4.

Algebra.Com

Question 618977: Prove that if �a� and �b� are odd positive integers, then a2+b2 is even but not divisible by 4.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If a is odd, it turns out that

. Similarly,

, so

, therefore it is even but not a multiple of 4.
RELATED QUESTIONS
Q.1) If a, b, c, are real numbers such that a2+2b=6, b2+4c= -7 and c2+6a= -13, then the... (answered by Edwin McCravy)

Let $P(x)$ be a nonconstant polynomial, where all the coefficients are nonnegative... (answered by jim_thompson5910)

Let P(x) be a nonconstant polynomial, where all the coefficients are nonnegative... (answered by Edwin McCravy,ikleyn)

given two odd integers 'a' and 'b'.prove that a^3-b^3 is divisible by 2^n iff a-b is... (answered by Alan3354)

Consecutive Integers If abcd are positive consecutive integers then is a+b^2+c^3 is... (answered by lynnlo,solver91311)

let 'a' and 'b' be a pair of positive integers whose highest common factor is 1.... (answered by richard1234)

Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime... (answered by Edwin McCravy)

If m and p are positive integers and (m+p) x m is even, which of the following must be... (answered by jim_thompson5910)

I am having a lot of trouble with these proofs; I get so far and alskdjfl.... prove or (answered by khwang)