Proving the Sum of Squares of Odd Numbers: Algebraic Method

[Trail_Builder]

Homework Statement

Prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

Homework Equations

n/a

The Attempt at a Solution

not really sure what to do so excuse my bad attempt

where n is an integer:

(1^2 + 1^2)/4 = n + 2


thnx for you help

as per rules, please only give one step away at a time and explain please :D thnx

 

[Dick]

Can you write me a formula for the nth odd number?

 

[turdferguson]

You need to replace those 1's with the general form of an odd number. Put all odd numbers in terms of all whole numbers and do the binomial expansion

 

[Trail_Builder]

oops yeh i found out i should have done 2n-1 lol

silly me, soz