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A4

Part of 1980 Putnam

Problems(1)

Putnam 1980 A4

Source: Putnam 1980

4/1/2022
a) Prove that there exist integers a,b,ca, b, c not all zero and each of absolute value less than one million, such that ∣a+b2+c3∣<10−11. |a +b \sqrt{2} +c \sqrt{3} | <10^{-11} . b) Let a,b,c a, b, c be integers, not all zero and each of absolute value less than one million. Prove that ∣a+b2+c3∣>10−21. |a +b \sqrt{2} +c \sqrt{3} | >10^{-21} .
Putnampigeonhole principlePutnam pigeonhole