prove that the square of any positive integers is of the form 5q,5q+1,5q+4for some integer q
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we know that
every positive integer is of the form 5m+r
Case 1
r = 0
(5m+0)^2
=25m
=5(5m)
=5q(q=5m)
Case 2
r=1
(5m+1)
=25m^2+1+10m{by (a+b)^2}
=5(5m^2+2m)+1
where q=5m^2m
similarly u have to prove other also but don't let r
more then 4
every positive integer is of the form 5m+r
Case 1
r = 0
(5m+0)^2
=25m
=5(5m)
=5q(q=5m)
Case 2
r=1
(5m+1)
=25m^2+1+10m{by (a+b)^2}
=5(5m^2+2m)+1
where q=5m^2m
similarly u have to prove other also but don't let r
more then 4
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