Question

prove that square of any positive integers of the fotm 5m+1 is of the same form

Answer 1

let a=bq+r , where b =5
possible remainders = 0,1,2,3,4
when r= 0
a=5q

when r=1
a=5m+1
squaring bothsides
a²= (5m+1)²
a²=25m²+ 10m+1
a²=5(5m²+2m) +1
a²=5m+1