Perfect Integers

An integer 'n' is called 'perfect' if it equals the sum of all its divisors 'd' ... {see attachment for complete definition and example} Let 'a' be a positive integer. Prove ... {see attachment}

Perfect Square; Perfect Cube; Perfect Fifth Power

Find the smallest positive integer N such that N/2 is a perfect square, N/3 is a perfect cube and N/5 is a perfect fifth power.

Euclid's Algorithm for Greatest Common Divisor

1. (a) Use the Euclidcan Algorithm to find the greatest common divisor of 13 and 21 (b) and (c) in attachment (PLEASE SEE ATTACHMENT FOR EXPLANATION OF EUCLID'S ALGORITHM AND COMPLETE PROBLEM)

Shuffle and Cardinality

(Bijection, shuffle, cardinality) Let (SYMBOL) = {0,1,2,3...N-1} where N is a positive integer ... (PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM)

Basic Algebra (subsitution)

Problem: Five children collect N pieces of Halloween candy and decide to split it evenly among them. When they try to divide it they have two pieces of candy left over. One of the children leaves, taking the 26 pieces of candy she collected with her. The remaining four children try to split the N-26 remaining pieces of candy and discover that they have one piece of candy left over. Frusterated, a second child leaves, taking 24 pieces of candy and the remaining three children split the N-26-24 pieces of candy left between them, delighted to discover that it can be split exactly three ways. What is the smallest (positive, of course) value for N for which this is possible? Are there other va... click for more