MathDB

5

Part of 2014 IMAC Arhimede

Problems(1)

natural numbers written a system with base a prime number

Source: IMAC Arhimede 2014 p5

5/6/2019
Let pp be a prime number. The natural numbers mm and nn are written in the system with the base pp as n=a0+a1p+...+akpkn = a_0 + a_1p +...+ a_kp^k and m=b0+b1p+..+bkpkm = b_0 + b_1p +..+ b_kp^k. Prove that (nm)≡∏i=0k(aibi)(modp){n \choose m} \equiv \prod_{i=0}^{k}{a_i \choose b_i} (mod p)
number theoryNumerical systemsSystemBinomialProductmoduloprime numbers