Find rational numbers a,b,c,d,e,f,g,h,i,j such that:

arithmetic/product.of.powers New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Find rational numbers a,b,c,d,e,f,g,h,i,j such that:

30^a * 31^b * 32^c * 33^d * 34^e * 35^f * 36^g * 37^h * 38^i * 39^j = 40

-- Mark van Hoeij <hoeij@sci.kun.nl>

Show solution

  a = 1,  c = 3/5,  g = -1/2

This is solved by factoring each integer, collecting like bases,
and setting all exponents to 0.  It is equivalent to a dimensional
analysis problem.

-- Joe Riel <jsr@sparc.sandiegoca.ncr.com> (September 1996)

[ Editor: the exponents not listed are 0.  Check: 30 * 32^(3/5) *
36^(-1/2) = 30 * 8 / 6 = 40. ]