#math trivia #67 solution

Burt Kaliski Jr. (@modulomathy)
3/7/12 8:17 AM
#math trivia for #March7: #67 divided by 366 = 1/p – 1/q + 1/r for p, q, r prime. What are the values of p, q and r?

Start by expressing 67/366 as a sum of fractions:

67/366 = 61/366 + 6/366 = 1/6 + 1/61.

The second fraction has a prime denominator, so can serve as 1/r. The first fraction’s denominator is composite, but can be replaced by a difference of fractions of the correct form:

67/366 = 1/2 – 1/3 + 1/61.

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