MATH 312 Midterm: MATH 312 2012 Winter Test 1
Document Summary
+ + 100!: suppose that n = 81294358x. Write down a digit in the slot marked. X so that n is divisible by a) 11 b) 9 c) 4: find all solutions of 7x 4 mod 13, de ne a carmichael number. Use the necessary and su cient con- dition for a number to be a carmichael number to show that 561 is a. Ii state whether the following are true or false with full justi cation. Iii find all positive integers n such that n! ends with exactly 74 zeros in decimal notation. Iv de ne the sum of divisors function (n) and number of divisors function (n). Show that there is no positive integer n with (n) = 14. V show that if a and b are relatively prime integers, then a (b)+b (a) 1 mod ab.
