MathDB

20

Part of 2019 India PRMO

Problems(2)

Number Theory / Sets

Source:

8/11/2019
Consider the set EE of all natural numbers nn such that whenn divided by 11,12,1311, 12, 13, respectively, the remainders, int that order, are distinct prime numbers in an arithmetic progression. If NN is the largest number in EE, find the sum of digits of NN.
number theorySetsprime numbersarithmetic sequence
Combi With Digits

Source: PRMO Leg 2 P20

8/25/2019
How many 4−4-digit numbers abcd‾\overline{abcd} are there such that a<b<c<da<b<c<d and b−a<c−b<d−cb-a<c-b<d-c ?
combinatoricsPRMO