Calculation shows that 250 100 mod 101 explain by what

Question

These problems are motivated by computational tasks in RSA encryption.

(a) Compute 2⁷⁴ mod 91 (note that 91 = 7 * 13).

(b) Find an a > 0 for which 14a = 1 mod 29.

(c) Calculation shows that 2⁵⁰ = 100 mod 101. Explain by what almost-true claim the number 101 is prime (you need not try possible factorizations of 101).

(d) Calculation shows that 2¹²⁵⁰ = 1844 mod 2501. Show that 2501 is not prime (you need not find the actual factors of 2501).