PPL 165 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
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Prize Problem LedgerZhi-Wei Sun prizesPPL 165Sun · A prime plus Pell numbers

Permanent problem IDPPL 165

Source-statedIndependentconjecture

Number theory

Sun · A prime plus Pell numbers

Every integer n>5 is the sum of an odd prime, a Pell number and twice a Pell number; the two Pell numbers may both be required positive.

prime numbersPell numbersadditive number theory
01

The problem

Every integer n>5 is the sum of an odd prime, a Pell number and twice a Pell number; the two Pell numbers may both be required positive.

Open since2009exact formulation date
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$1,000 proof · $100 counterexampleZhi-Wei Sun
Personal offer

US$1,000 is offered for the first positive solution published in a well-known mathematical journal; US$100 for the first explicit counterexample that the author can verify by computer.

Award source ↗
03

Sources & reading

2 unique reference linksAuthor’s refereed-paper preprint OEIS A000129
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Related open targets

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