Power play
In the following, “^” means is raised to the power of, so 6^2 = 36. When ((2^3)^4)^5, 2^((3^4)^5) and 2^(3^(4^5)) are each divided by 13, the remainders are respectively p, q and r.
What is the absolute difference between (p+q)^r and r^(p+q)?
WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 6 February. The Editor’s decision is final. Please send entries to Enigma 1731, New Scientist, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
Answer to 1725 Square bashing: The smallest number is 12492501
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The winner A. Giannakopoulos of Filton, Gloucestershire, UK
