Proving the Sum of Squares of Odd Numbers: Algebraic Method

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Homework Help Overview

The original poster attempts to prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4. The discussion revolves around algebraic methods and properties of odd numbers.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the need to express odd numbers in a general form and consider the implications of using binomial expansion. The original poster expresses uncertainty about their initial approach.

Discussion Status

Some participants have provided guidance on how to represent odd numbers and suggested refining the original poster's approach. There is an acknowledgment of a mistake in the initial attempt, leading to further exploration of the topic.

Contextual Notes

The original poster mentions homework rules that limit the assistance to one step at a time, indicating a structured approach to the problem-solving process.

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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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