RPS #002 - Looks Familiar?

Number Theory Level 3

Let A = { x ∣ x = 2 k + 5 m , k , m ∈ N 0 } A = \{x | x = 2k + 5m , k,m \in N_0\} . Find the sum of all positive integers which is not the elements of A A .

(Note that N 0 = { 0 , 1 , 2 , 3 , . . . } N_0 = \{0,1,2,3,...\}


The answer is 4.

Rimba Erlangga by Rimba Erlangga , 23, Indonesia

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1 solution

It's just basic use of Chicken McNugget Theorem . So the largest number that can not be achieved is p q − p − q pq-p-q , here p = 5 , q = 2 p=5 ,q=2

It comes out to be 10 − 5 − 2 = 3 10 - 5 - 2 = 3 the only other number that cannot be achieved using 2 k + 5 m 2k+5m is 1 .

Therefore the sum is 4 .

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