Prove or disprove: Any integer n can be written as 5k + 2l

[Mooch22]

Help, please! I need to prove or disprove the following:

Any integer n can be written as 5k + 2l for some integers k and l.

 

[pka]

to prove the following: Any integer n can be written as 5k + 2l for some integers k and l.

Suppose n is odd then n-5 is even and is 2k for some k: 2k+5(1)=n.
Suppose n is even then n=2j for some j and 2j+5(0)=n.

 

[stapel]

Duplicate thread deleted.

If you would like additional help, it would be better to show how far you've gotten with what you've already been given. Thank you.

Eliz.

 

[bbking22]

n=5k+2l=2*2k+k+2l=k+2(l+2k). Choosing l=-2k , then we have n=k. Thus for every n there are k,l such that n=5k+2l (there is at least one pair of them: k=n and l=-2k=-2n). The question is how many are the possible pairs (as a function of the integer)?