- #1
tennesseewiz
- 21
- 0
Homework Statement
For all integers m, m[tex]^{}2[/tex]=5k, or m[tex]^{}2[/tex]=5k+1, or m[tex]^{}2[/tex]=5k+4 for some integer k.
Relevant equations
I'm pretty sure we have to use the Quotient Remainder THM, which is:
Given any integer n and positive integer d, there exists unique integers q and r such that,
n=dq+r and 0 [tex]\leq[/tex]r<d.
But that's as far as I got. I have no idea what to do next.
For all integers m, m[tex]^{}2[/tex]=5k, or m[tex]^{}2[/tex]=5k+1, or m[tex]^{}2[/tex]=5k+4 for some integer k.
Relevant equations
I'm pretty sure we have to use the Quotient Remainder THM, which is:
Given any integer n and positive integer d, there exists unique integers q and r such that,
n=dq+r and 0 [tex]\leq[/tex]r<d.
But that's as far as I got. I have no idea what to do next.