MathDB

1

Part of 1990 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

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

Source: I - Rioplatense 1990 L3 P1

9/19/2022
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)
floor functionalgebradiophantine