Mark each of the following true or false.
__ a. ap-l = 1 (mod p) for all integers a and primes
__ b. ap-1 = 1 (mod p) for all integers a such that a ^ 0 (mod p) for a prime p.
__ c. φ(n)
+. __ d. φ(n)
+. __ e. The units in ℤ„ are the positive integers less than n and relatively prime to n.
__ f. The product of two units in ℤn is always a unit.
__ g. The product of two nonunils in ℤn may be a unit.
__ h. The product of a unit and a nonunit in ℤn is never a unit.
__ i. Every congruence ax = b (mod p), where p is a prime, has a solution.
__ j. Let d be the gcd of positive integers a and m. If d divides b, then the congruence ax = b (mod m)
has exactly d incongruent solutions.
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