Problem of the Week

Rodin's "Thinker" contemplates the problem of the week.

WEEK THREE: Divisor Diversions

Solutions due by high noon on Friday, February 15, 2013.

We say that two positive integers a and b are "chummy" if each one divides into 1 more than the square of the other.  For instance, 2 and 5 are chummy since 2 divides into 5²+1=26, while 5 divides into 2²+1=5.

• Explain why 3 is not chummy with any other positive integer.
• Find a pair of two-digit chummy numbers.
• Prove that there is an infinite sequence of numbers a₁, a₂, a₃, ... such that each number in the sequence is chummy with the next.

This problem is brought to you by Sam Vandervelde.

Submit your solutions to Maegan Bos.  You may submit either a hard copy or an electronic file.  Good luck!

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