MathDB

P1

Part of 2023 Bangladesh Mathematical Olympiad

Problems(2)

Diophantine factorial

Source: BdMO 2023 Secondary National P1

2/12/2023
Find all possible non-negative integer solution (x,y)(x,y) of the following equation- x!+2y=(x+1)!x! + 2^y =(x+1)! Note: x!=x⋅(x−1)!x!=x \cdot (x-1)! and 0!=10!=1. For example, 5!=5×4×3×2×1=1205! = 5\times 4\times 3\times 2\times 1 = 120.
factorialnumber theoryDiophantine Equations
Diophantine Factorial

Source: BdMO 2023 Higher Secondary National P1

2/12/2023
Find all possible non-negative integer solution (x,x, yy) of the following equation- x!+2y=z!x!+2^y=z! Note: x!=x⋅(x−1)!x!=x\cdot(x-1)! and 0!=10!=1. For example, 5!=5×4×3×2×1=1205!=5\times4\times3\times2\times1=120.
factorialnumber theoryDiophantine equation