Brilliant digital coins

Number Theory Level 2

BrilliantCoin is a new digital currency that can be used to make payments to Brilliant. There are two types of BrilliantCion with values 92 and 504 92 \ \text{and} \ 504 . You can make a payment by using only these coins. It is allowed to transfer money from/to Brilliant account from your digital wallet (you do have enough money). Which of the following payments can't be made?

124 514 840 600 620

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Ossama Ismail
Dec 29, 2017

Ans: 514

Only an amount of money which is divided by G C D ( 92 , 504 ) \color{#3D99F6} GCD(92,504) can be made.

G C D ( 92 , 504 ) = 4 GCD(92,504) = 4

Ref: Bezout's Lemma : For nonzero integers n and m, let d be the greatest common divisor(n, m). Then, there exist integers x and y such that

n x + m y = d nx + my = d

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