Extra Credit Problem #1.

The following problem was suggested by Michael O’Neill (who is in our section of 119):

1. Take any positive integer whose last digits is 5. For example 715.

2. Drop the 5. Call the resulting number n. So here n = 71.

3. Take the product of n and n+1. So here we get 71 time72 = 5112.

4. Multiply this number by 100 and then add 25. So here we get 511200+25=511225.

PROBLEM: Explain very clearly in writing why the resulting number will always be the square of the original number. (So in the example, 511225 = 715 times 715. ) If you think this is not true then come up with a counter-example.

POINTS: The first two people to hand in a solution get 2 pts towards a quiz grade. (Quizzes are worth 10 points each.)