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Diophantine factorial

Source: BdMO 2023 Secondary National P1

February 12, 2023

factorialnumber theoryDiophantine Equations

Problem Statement

Find all possible non-negative integer solution

(x,y)

of the following equation-

x! + 2^y =(x+1)!

Note:

x!=x \cdot (x-1)!

and

0!=1

. For example,

5! = 5\times 4\times 3\times 2\times 1 = 120

.

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