# Monthly Archives: October 2010

## 9876 Power

What would be the units (ones) digit for raised to the power or ? Source: http://www.olemiss.edu 9/20/2010 Solution 30=1 34=81 38=6561 312=531441 316=43046721 31=3 35=243 39=19683 312=1594323 317=129140163 32=9 36=729 310=59049 314=4782969 318=387420489 33=27 37=2187 311=177147 315=14348907 319=1162261467 Notice that … Continue reading

## First Term

In an arithmetic sequence of positive whole numbers, the common difference is twice the first term of the sequence.  If the sum of the first six terms is equal to the square of the first term of the sequence, what … Continue reading

## 823

Let  and represent different positive integers.  Find the value of and if ? Source: mathcontest.olemiss.edu 10/25/2010 Solution  is a prime number, that is . We can write Therefore, and .

## 100737

P and Q represent different positive integers.  Find all values of both P and Q such that the product of the product of P and Q and the difference of P less Q is equal to 100737.  In other words, … Continue reading