MathDB

3

Part of 2018 India Regional Mathematical Olympiad

Problems(2)

Decimal expansion of a rational

Source: RMO 2018 P3

10/7/2018
For a rational number rr, its *period* is the length of the smallest repeating block in its decimal expansion. for example, the number r=0.123123123...r=0.123123123... has period 33. If SS denotes the set of all rational numbers of the form r=abcdefgh‾r=\overline{abcdefgh} having period 88, find the sum of all elements in SS.
algebracombinatorics
Finally a NT in RMO

Source: RMO 2018 P3

10/28/2018
Show that there are infinitely many tuples (a,b,c,d)(a,b,c,d) of natural numbers such that a3+b4+c5=d7a^3 + b^4 + c^5 = d^7.
number theory