On A^4 + B^4 + C^4 = D^4¶
Elkies, N. D. (1988). On A^4 + B^4 + C^4 = D^4. Mathematics of Computation, 825-835.
Cited by¶
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Primes¶
- Negative Case Analysis
- The hunt — eventually a computer search — finds one: \(95800^4 + 217519^4 + 414560^4 = 422481^4\), a sum of three fourth powers equal to a fourth power.
This sourceProvides infinitely many counterexamples to Euler's conjecture for fourth powers via elliptic curves, and reports the smallest such solution (95800^4 + 217519^4 + 414560^4 = 422481^4, found by Frye), with the elliptic-curve structure showing the counterexamples cluster rather than scatter.
- The hunt — eventually a computer search — finds one: \(95800^4 + 217519^4 + 414560^4 = 422481^4\), a sum of three fourth powers equal to a fourth power.
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