Abstract
Beal's Conjecture : The equation za = xb+yc has no solution in relatively prime positive integers x; y; z with a, b and c odd primes at least 3. A proof of this longstanding conjecture is given.
Highlights
Suppose zξ = xμ + yν is true for any relatively prime positive integers x, y, z and odd primes ξ, μ and ν with ξ, μ, ν at least 3
Beal’s Conjecture: The equation zξ = xμ + yν has no solution in relatively prime positive integers x, y, z with ξ, μ and ν odd primes at least 3
The case when yν is even is similar to the case when xμ is even
Summary
Suppose zξ = xμ + yν is true for any relatively prime positive integers x, y, z and odd primes ξ, μ and ν with ξ, μ, ν at least 3. Y and z are relatively prime, (zξ), (xξ) and (yξ) are relatively prime. It is clear that if (zξ)ξ = (xμ)ξ + (yν)ξ, either xμ or yν or zξ is divisible by 2.
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