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Arithmetic Numbers Enumeration (Posted on 2014-12-19) Difficulty: 3 of 5
Consider five positive integers A < B < C < D < E in arithmetic sequence, and find all possible solutions of:
A4 + B4 + C4 + D4 = E4 - 143

No Solution Yet Submitted by K Sengupta    
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Solution solution Comment 2 of 2 |
Letting p equal the constant in the arithmetic progression, a quartic polynomial can be formed:
3A4 + (8p)A3 + (-12p2)A2 + (-112p3)A + (143 - 158p4) = 0

Solving the quartic for p=1, the two real roots are (3, ≈-66/485).
Iterating through different constants and values of A (using a computer program) found no other solutions.
As A and p (by inference) are given to be positive integers:
A = 3, B = 4, C = 5, D = 6, and E = 7.



Edited on December 19, 2014, 4:16 pm
  Posted by Dej Mar on 2014-12-19 16:14:16

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