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

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then

(2n+1)² + (2n+3)²

= 8n² + 16n + 10

divide this by 2 because you can...

4n²+8n+5

now what? thanks to whoever replies

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then

(2n+1)² + (2n+3)²

= 8n² + 16n + 10

divide this by 2 because you can...

4n²+8n+5

now what? thanks to whoever replies

manps

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

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then

(2n+1)² + (2n+3)²

= 8n² + 16n + 10

divide this by 2 because you can...

4n²+8n+5

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then

(2n+1)² + (2n+3)²

= 8n² + 16n + 10

divide this by 2 because you can...

4n²+8n+5

let the odd numbers be 2n+1 and 2n+1

then...

(2n+1)² + (2n+1)²

= 2(4n² + 4n + 1)

= 8n² + 8n + 2

- remainder 2 at the end.

manps

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

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then

(2n+1)² + (2n+3)²

= 8n² + 16n + 10

divide this by 2 because you can...

4n²+8n+5

now what? thanks to whoever replies

Ok so lets say the odd numbers are, 2n+1 and 2n+3

then

(2n+1)² + (2n+3)²

= 8n² + 16n + 10

divide this by 2 because you can...

4n²+8n+5

now what? thanks to whoever replies

use two different odd numbers not consecutive...call odd number one 2n+1 and number two 2m+1

You have to account for it being ANY two odd numbers. So, A = (2a+1) and B = (2b+1)

So, A^2 + B^2 = 4a^2 +4a^ +1 + 4b^2 + 4b + 1

= 4(a^2 + a + b^2 + b) + 2

So, A^2 + B^2 = 4a^2 +4a^ +1 + 4b^2 + 4b + 1

= 4(a^2 + a + b^2 + b) + 2

Dekota

let the odd numbers be 2n+1 and 2n+1

then...

(2n+1)² + (2n+1)²

= 2(4n² + 4n + 1)

= 8n² + 8n + 2

- remainder 2 at the end.

then...

(2n+1)² + (2n+1)²

= 2(4n² + 4n + 1)

= 8n² + 8n + 2

- remainder 2 at the end.

you havent divided by 4

--------------

Da Bachtopus

You have to account for it being ANY two odd numbers. So, A = (2a+1) and B = (2b+1)

So, A^2 + B^2 = 4a^2 +4a^ +1 + 4b^2 + 4b + 1

= 4(a^2 + a + b^2 + b) + 2

So, A^2 + B^2 = 4a^2 +4a^ +1 + 4b^2 + 4b + 1

= 4(a^2 + a + b^2 + b) + 2

ok but you havent divided by 4

manps

ok but you havent divided by 4

2n+1 2n-1

(2n+1)^2 + (2n-1)^2

expand-

[(4n^2 +2n+2n+1)] + [(4n^2 -2n-2n-1)]

then I collected my like terms

which gave me

8n^2 then I divided it by 4

which gave me 2n^2 and the 2 before the n shows that dividing it by 4 would leave a remainder of 2

(2n+1)^2 + (2n-1)^2

expand-

[(4n^2 +2n+2n+1)] + [(4n^2 -2n-2n-1)]

then I collected my like terms

which gave me

8n^2 then I divided it by 4

which gave me 2n^2 and the 2 before the n shows that dividing it by 4 would leave a remainder of 2

Original post by jellybean636

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- Easy Maths modules at University
- Maths vs Maths and Physics
- What’s some hard university maths content?
- How to get better at BMO1
- Road to a 2:1 - 2nd year maths GYG
- repeating 1s quadratic
- Maths a level proofs (edexcel) tips
- Will sociology affect my chances?
- 'solutions relying entirely on calculator technology are not acceptable'
- Westminster 16+ further maths
- maths degree - help - about maths degree
- Do you think A Level Maths has enough proof in it?
- Second undergrad - Liv Uni / Carmel College
- In my personal statement, what if I want to apply to two distinct subjects??
- Topics to study before computer science
- cubic one root proof
- Concerns about my Maths degree
- Step ii 2024
- Biomedical Eng vs Chem Eng vs EEE vs CompSci
- How should I go about preparing for the STEP Maths exam?

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