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9.8

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(2)

perfect squares with different digits (V Soros Olympiad 1998-99 Round 1 9.8)

Source:

5/25/2024
Find all natural numbers whose decimal notation consists of different digits of the same parity and which are perfect squares.
number theoryPerfect Squares
f(\sqrt[3]{2}-1) (V Soros Olympiad 1998-99 Round 3 9.8)

Source:

5/25/2024
Calculate f(23−1)f(\sqrt[3]{2}-1) , where f(x)=x1999+3x1998+4x1997+2x1996+4x1995+2x1994+...f(x) = x^{1999} + 3x^{1998} + 4x^{1997} + 2x^{1996} + 4x^{1995} + 2x^{1994} + ... ...+4x3+2x2+3x+1.... + 4x^3 + 2x^2 + 3x+ 1.
algebrapolynomial