DISINI exam2002
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F or an arbitrary real number x, we dene [x℄ to be the greatest integer. less than or equal
F or eah real number , we dene b to be the greatest integer whih.. is less than or
(a) Find five positive integers, not necessarily different, whose sum is equal to their product.. (b) Show that the problem in (a) has at least
(4) Show that there exists a positive integer N such that for all integers a > N , there exists a contiguous substring of the decimal expansion of a that is divisible
The turtle begins in a corner square of the grid and enters each square exactly once, ending in the square where she started.. In terms of n, what is the largest positive integer k
• On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed. • If Carolyn cannot remove any more numbers, then
The diagram below shows six distinct positive integers in a ring and the sum of any two neighboring numbers is a perfect square. The below diagram is to be filled with six
(c) Let’s say that an integer N > 1 is really friendly if N cannot be written as the sum of two, or three, or four, or any number of positive integers without using at least one
