Importance: High ✭✭✭
Keywords: beals conjecture
Recomm. for undergrads: no
Posted by: lalitha
on: April 23rd, 2013
Solved by: lalitha

If A(pwr)x+B(pwr)y=C(pwr)z where A,B,C,x,y,z are positive integers and x,y,z>=2,then A,B,C must have a common prime factor.

we need to show A(pwr)x+B(pwr)y != C(pwr)z to disprove it. let us take A(pwr)x+B(pwr)y where A is an odd no. and B is an even no. and x,y>=3 then apply power to A(odd number) gives an odd number apply power to B (even number) gives an even number OR ELSE let us take A(pwr)x=2n+1 B(pwr)y=2n the addition of Ax+By gives an odd number =>2n+1+2n =4n+1……(1) where n€odd numbers.substitute odd number in (1),we get an odd number which cannot be shown as a number’s power the result must be a constan


* indicates original appearance(s) of problem.


For those interested, the statement of the problem is wrong and the step "let us take A(pwr)x=2n+1 B(pwr)y=2n" is incorrect (there may exist no such n). The following Aaronson signs apply: 1, 2, 3 (would imply no triples rather than no coprime triples), 6, 7, and 10.

beals conjecture

why dont we take A(pwr)x=2n+1 and B(pwr)y=2n.he said to add 2 co-primes dnt even&odd numbers are co-prime.iam representing odd number as 2n+1 and even number as 2n

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