Possible primes of 2018

Number Theory Level 3

a b − c d = 2018 \large a^b - c^d =2018 If a , b , c a, b , c and d d are distinct primes where a < b a < b and d < c d < c .

Find the value of a + b + c + d a+b+c+d .


The answer is 25.

Naren Bhandari by Naren Bhandari , 21, India

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2 solutions

3 7 − 1 3 2 = 2018 3^7-13^2=2018

Therefore, a = 3 , b = 7 , c = 13 , d = 2 a=3,b=7,c=13,d=2

a + b + c + d = 25 a+b+c+d=\boxed{25}

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do you know the way to find the numbers formally, those numbers are easy to find because theyre small, what if the numbers are big numbers like 101 etc

Wage Mareto - 3 years, 3 months ago
Giorgos K.
Mar 1, 2018

A quick search in Mathematica. using only the first 10 primes,

Select[Permutations[Prime@Range@10,{4}],#1^#2-#3^#4&@@#==2018&]

returns {3, 7, 13, 2}

these are the {a,b,c,d}

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