MathDB

B3

Part of 2018 Malaysia National Olympiad

Problems(3)

Removing a factorial to form a square

Source: OMK 2015 Sulong, Section B Problem 3

6/21/2021
There are 200200 numbers on a blackboard: 1!,2!,3!,4!,......,199!,200! 1! , 2! , 3! , 4! , ... ... , 199! , 200!. Julia erases one of the numbers. When Julia multiplies the remaining 199199 numbers, the product is a perfect square. Which number was erased?
number theoryfactorial
OMK 2018 Muda, Section B Problem 3

Source: OMK 2018 Muda, Section B Problem 3

6/21/2021
Let nn be an integer greater than 11, such that 3n+13n + 1 is a perfect square. Prove that n+1n + 1 can be expressed as a sum of three perfect squares.
number theoryPerfect Squares
2018 ones in a row 2018 Malaysia OMK Juniors B3

Source:

9/19/2021
Given 20182018 ones in a row: 1   1   1   1   ...   1   1   1   1⏟2018   ones\underbrace{1\,\,\,1\,\,\,1\,\,\,1 \,\,\, ... \,\,\,1 \,\,\,1 \,\,\,1 \,\,\,1}_{2018 \,\,\, ones} in which plus symbols (+)(+) are allowed to be inserted in between the ones. What is the maximum number of plus symbols (+)(+) that need to be inserted so that the resulting sum is 8102?
combinatorics