Friday

December 19, 2014

December 19, 2014

Posted by **romulo** on Wednesday, March 7, 2007 at 1:45am.

Proposition: That 4k (k is any integer) = a^2 +2b^2, and a is even, and b is odd.

But 4k is even (product of any integer and 4), so a^2 must be even, as 2b^2 is even.

Dividing both sides by 4,

k=a^2/4 + 2b^2/4

but a is even, so a=2*n where n is an integer. a^2=4n^2

k= n^2 + b^2/2

But b is odd, so b^2/2 is not an integer.

Therefore, k cannot be an integer, so the proposition is contradicted.

**Answer this Question**

**Related Questions**

Discrete Math - 1. Assume that n is a positive integer. Use the proof by ...

discrete math - prove that if n is an integer and 3n+2 is even, then n is even ...

DISCRETE MATHS - We need to show that 4 divides 1-n2 whenever n is an odd ...

Algebra - The sum of two consecutive odd integers is 56. A. Define a variable ...

maths - prove that any odd positive integer of 8q+1,where q is any integer?

Algebra - The sum of two consecutive even integers is 118. A. Define a variable ...

DISCRETE MATHS - Prove that if n is an odd positive integer, then 1 ≡ n2 (...

Discrete Mathematics - Prove that if n is an odd positive integer, then 1 ≡...

math - if the number represented by n-3 is an odd integer, which expression ...

algebra - Kayla Wants To write an Expression that will always produce an odd ...