Find several integers that are congruent to 5 modulo 6 and t

Find several integers that are congruent to 5 modulo 6 and then square each of these integers. For each integer m from Part (a), determine an integer k so that 0 lessthanorequalto k

Solution

a.

5,11,17,23

5^2=25=1 mod 6

11^2=121=1 mod 6

17^2=289=1 mod 6

23^2=529=1 mod 6

b)

k=1

c)

For each integer m, if m=5 mod 6 then m^2=1 mod 6

d.)

Let, m=5 mod 6

m=6k+5

m^2=(6k+5)^2=36k^2+25+60k=36k^2+24+60k+1=1 mod 6

Hence proved