Let us pair the squares of the numbers 1 to n with the squares of the numbers n+1 to 2n such that each pair sums up to a prime.
1. Demonstrate that it is not possible for n1=3, n2=?(find out) and n3=??(find out)
2. For what value of n there are exactly 2 ways to perform the task?
Hint: all answers are below 15
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Submitted by Ady TZIDON
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Solution:
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1. It is possible for n=2; impossible for 3,6,11
2. a(5) = 2 because there are two ways: (1,4,9,16,25) + (36,49,100,81,64) = (37,53,109,97,89) and (1,4,9,16,25) + (100,49,64,81,36) = (101,53,73,97,61).
source: A077762,
see Charlie's solution for more details. |
