Does there exist a , b , c , d such that a +

grinder3yve0

grinder3yve0

Answered question

2022-06-02

Does there exist a , b , c , d such that a + b + c + d 4 is an integer?
Let a , b , c , d are different positive integers, such that a,b,c, nor d is a multiple of a different variable.
Question:
Does there exist a , b , c , d for
a + b + c + d 4 = I
such that I is an integer?

Answer & Explanation

Halle Mckee

Halle Mckee

Beginner2022-06-03Added 4 answers

One way is to find two primes that are 1 mod 4 and two primes which are 3 mod 4.
For instance, 5,7,11,13.
Sufirk6u38

Sufirk6u38

Beginner2022-06-04Added 1 answers

Just make them all one more than a multiple of 4; for example
( a , b , c , d ) = ( 5 , 9 , 13 , 17 ). This isn't the only way, but it's certainly one way.

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