Question

Aratati ca ultima cifra a produsului dintre 2 nr. naturale consecutive nu poate fi decat 0, 2 sau 6 (luati toate cazurile particulare si scrietile )(sunt doar 10 ) dau orice

Answer 1

n(n+1), U(n)={0,1,2,3,4,5,6,7,8,9}, U(n+1)={1,2,3,4,5,6,7,8,9,0}

U(0x1)=0. ultima cifra a produsului dintre n cu ultima cifra 0 si numarului urmator
U(1x2)=2 ...........................................................................................1........................
U(2x3)=6 ...........................................................................................2......................
U(3x4)=2............................................................................................3.......................
U(4x5)=0............................................................................................4........................
U(5x6)=0............................................................................................5........................
U(6x7)=2............................................................................................6........................
U(7x8)=6............................................................................................7........................
U(8x9)=2.............................................................................................8........................
U(9x10)=0...........................................................................................9.........................

U[n(n+1)]={0,2,6}