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A325421
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Numbers k coprime to 10 such that there are exactly two values of A for which k^2+4*A and k^2-4*A are perfect squares.
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0
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169, 289, 507, 841, 867, 1183, 1369, 1521, 1681, 1859, 2023, 2523, 2601, 2809, 3179, 3211, 3549, 3721, 3887, 4107, 4563, 5043, 5239, 5329, 5491, 5577, 5887, 6069, 6647, 7267, 7569, 7803, 7921, 7943, 8281, 8427, 8959, 9251, 9409, 9537, 9583, 9633, 9971
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OFFSET
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1,1
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COMMENTS
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These are the odd integers k, not a multiple of 5, such that k^2 is an arithmetic mean of two other odd perfect squares in exactly two ways.
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LINKS
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EXAMPLE
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169 is a term since 169^2±4*(5070) and 169^2±4*(7140) are all perfect squares.
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PROG
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(PARI) ok(k)={if(k%2==0||k%5==0, 0, my(k2=k^2, L=List()); forstep(i=1, k-1, 2, my(d=k2-i^2); if(issquare(k2+d), listput(L, i))); #L==2)}
for(k=1, 10000, if(ok(k), print1(k, ", "))) \\ Andrew Howroyd, Sep 06 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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