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A338800
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Smallest number that is the sum of two distinct n-th powers of primes in two different ways.
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1
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OFFSET
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1,1
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COMMENTS
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The Lander, Parkin, and Selfridge conjecture implies that for n >= 5 a number can be the sum of two n-th powers of positive integers in at most one way, and in particular that a(n) does not exist for n >= 5. - Robert Israel, Nov 13 2020
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LINKS
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EXAMPLE
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16 = 3 + 13 = 5 + 11.
410 = 7^2 + 19^2 = 11^2 + 17^2.
6058655748 = 61^3 + 1823^3 = 1049^3 + 1699^3.
3262811042 = 7^4 + 239^4 = 157^4 + 227^4.
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MAPLE
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f:= proc(n) local S, P, p, pn, b;
S:= {}:
P:= {}:
p:= 1:
b:= infinity;
do
p:= nextprime(p);
pn:= p^n;
if pn > b then return b fi;
V:= select(`<`, map(`+`, P, pn), b);
newv:= V intersect S;
S:= S union V;
P:= P union {p^n};
if newv <> {} then
b:= min(newv);
S:= select(`<`, S, b);
P:= select(`<`, P, b);
fi;
od:
end proc:
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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