Can any number of the form \(\displaystyle{4}{k}+{2}\)

Rubi Reid

Rubi Reid

Answered question

2022-03-18

Can any number of the form 4k+2 be written as a2+b2c2d2?

Answer & Explanation

Jamiya Bradford

Jamiya Bradford

Beginner2022-03-19Added 6 answers

Step 1
The sequence of nonnegative integers not congruent to 2 mod 4. It is also the nonnegative integers that can be written as a difference of two integer squares.
Thus for all n not of the form 4k+2 we have n=a2b2 and for those of the form 4k+2 we have n=a2+12b2. Thus, for all nonnegative integers n we can find integers a,b,c,d such that n=a2+b2c2d2.
hofirati8y9

hofirati8y9

Beginner2022-03-20Added 3 answers

Step 1
Here is one way:
4k+2=(k+1)2+(k+1)2k2k2

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