January+31

Q1

Find math 2^{220} \mod 221 math Conclude that 221 is composite.

Q2

Show that math a^{48} \equiv 1 \mod 221 math for all a relatively prime to 221.

Q3

Solve the congruence math x^7\equiv 3 \mod 21. math

Q4

Show that the congruence math x^2=a \mod 21 math can have 0, 1, 2 or 4 solutions depending on a.