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[x/10]=[x/11]+1

Source: I - Rioplatense 1990 L3 P1

September 19, 2022
floor functionalgebradiophantine

Problem Statement

How many positive integer solutions does the equation have ⌊x10⌋=⌊x11⌋+1?\left\lfloor\frac{x}{10}\right\rfloor= \left\lfloor\frac{x}{11}\right\rfloor + 1? (⌊x⌋\lfloor x \rfloor denotes the integer part of xx, for example ⌊2⌋=2\lfloor 2\rfloor = 2, ⌊π⌋=3\lfloor \pi\rfloor = 3, ⌊2⌋=1\lfloor \sqrt2 \rfloor =1)
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