Proving the Sum of Squares of Odd Numbers: Algebraic Method

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The discussion focuses on proving that the sum of the squares of any two odd numbers results in a remainder of 2 when divided by 4. Participants suggest using the general form of odd numbers, represented as 2n - 1, for the proof. There is an emphasis on algebraic methods and binomial expansion to derive the formula. One user acknowledges a previous mistake in their approach and seeks clarification on the correct formula for odd numbers. The conversation highlights the importance of step-by-step guidance in solving the problem.
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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
 
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Can you write me a formula for the nth odd number?
 
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
 
oops yeh i found out i should have done 2n-1 lol

silly me, soz
 

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