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A261782 Powers C^z = A^x + B^y with positive integers A,B,C,x,y,z such that x,y,z > 2. 4
16, 32, 64, 128, 243, 256, 512, 1024, 2048, 2744, 4096, 6561, 8192, 16384, 32768, 65536, 131072, 177147, 185193, 262144, 474552, 524288, 614656, 810000, 941192, 1048576, 1124864, 1419857, 1500625, 2097152, 3241792, 4194304 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Beal's conjecture states that A, B, and C have a common prime factor.

LINKS

Anatoly E. Voevudko and Charles R Greathouse IV, Table of n, a(n) for n = 1..1229 (first 196 terms from Voevudko)

American Mathematical Society, Beal Prize

Anatoly E. Voevudko, Description of all powers in b245713

Anatoly E. Voevudko, Description of all powers in b261782

Wikipedia, Beal's conjecture

EXAMPLE

2^3 + 2^3 = 2^4.

PROG

(PARI) is(n)=if(ispower(n)<3, return(0)); for(x=3, logint((n+1)\2, 2), for(A=2, sqrtnint(n, x), if(ispower(n-A^x)>2, return(1)))); 0 \\ Charles R Greathouse IV, Sep 03 2015

(PARI) list(lim)=my(v=List(), u=v, t); for(z=3, logint(lim\=1, 2), for(C=2, sqrtnint(lim, z), listput(v, C^z))); v=Set(v); for(i=1, #v, for(j=i, #v, t=v[i]+v[j]; if(t>lim, break); if(setsearch(v, t), listput(u, t)))); Set(u) \\ Charles R Greathouse IV, Sep 03 2015

CROSSREFS

Subsequence of A076467.

Cf. A245713.

Sequence in context: A197917 A317475 A239751 * A256818 A048170 A067053

Adjacent sequences:  A261779 A261780 A261781 * A261783 A261784 A261785

KEYWORD

nonn

AUTHOR

Anatoly E. Voevudko, Aug 31 2015

STATUS

approved

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Last modified January 29 01:49 EST 2020. Contains 331328 sequences. (Running on oeis4.)