number theory

a|1 if and only if ……………

The Diophantine equation
 $6x+51y=22$  has .................  solns

The lcm(a,b) =ab if and only if …………………

Let a=qb+r and if r=0, then b/a and gcd(a,b)= …………..

If a|b then a|bc.

Identify the solutions of the linear congruence 9x≡21(mod30).

The linear congruence ax≡b(mod n) has how many solutions if gcd(a,n)=1

The linear congruence 36x≡8(mod102) has no solution

16!≡…………………..(mod 17)

In division algorithm, the possible remainders of r when b=2 are …………….