Problem 44

Projekt Euler w Ruby
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Problem 44

Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, …

It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference is pentagonal and D = |Pk − Pj| is minimised; what is the value of D?

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class Integer def p self*(3*self-1)/2 end def p? return ((Math::sqrt(24*self+1)+1)/6)%1==0 end end (1..1_00_000).each do |j| (j..1_00_000).each do |k| if (k.p+j.p).p? && (k.p-j.p).p? p (k.p-j.p) break end end end