These problems are motivated by computational tasks in RSA encryption. (a) Compute 2^74 mod 91 (note that 91 = 7 * 13). (b) Find an a > 0 for which 14a = 1 mod 29. (c) Calculation shows that 2^50 = 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 2^1250 = 1844 mod 2501. Show that 2501 is not prime (you need not find the actual factors of 2501)