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Part of 2015 May Olympiad

Problems(2)

erase 2 numbers with prime sum 1-510 May Olympiad (Olimpiada de Mayo) 2015 L2 P4

Source:

510

positive integers are written on a blackboard:

1, 2, 3, ..., 510

. An operation consists of of erasing two numbers whose sum is a prime number. What is the maximum number of operations in a row what can be done? Show how it is accomplished and explain why it can be done in no more operations.

combinatoricsprimenumber theory

no=13 x (sum of digits) May Olympiad (Olimpiada de Mayo) 2015 L1 P4

Source:

We say that a number is superstitious when it is equal to

13

times the sum of its digits . Find all superstitious numbers.

sum of digitsDigitsnumber theory