Computation Workshop Solution Checker
Counting Triples
For each integer \( N \), let \( A(N) \) denote the number of ordered triples \( (x,y,z) \) of integers such that \( x^3 + y^3 + z^3 - 3xyz = N \). For example \( A(1) = 3 \) because there are three triples: \( (1,0,0), (0,1,0), (0,0,1) \).
| Part A |
Determine \(A(28)\) |
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| Part B |
Determine \(A(9828)\) |
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Prome Numbers
A "Prome" number is any prime number consisting of only odd digits. For example 177 is a prome because it is prime and all its digits ("1", "7" and "7") are all odd. Whereas 163 is not a prome because "6" is even. Let \(S(N)\) denote the sum of all prome numbers less than \(N\). For example \(S(40) = 3+5+7+11+13+17+19+31+37 = 143\).
| Part A |
Determine \(S(1000)\) |
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| Part B |
Determine \(S(10^8)\) |
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