Natural Arithmetic Progression
Number Theory
Level
3
A, B, C, D, E are 5 natural numbers in an arithmetic progression.
The sum of A, B, C, D, E is a cube of a natural number.
The sum of B, C, D is the square of a natural number.
What could be the minimum value of C?
The answer is 675.
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1 solution
A+E =2C,B+D=2C,A+B+C+D+E=5C=Y^3=Y . Y .Y
B+C+D=N^2=N .N=3C WHICH MEANS
C=3K
AS 5C=Y^3
C=25J
AS C=3K
AND 5C IS A CUBE OR HUB
IT MEANS THAT C HAS AT LEAST 3 FACTORS 3
SO C, IS AT LEAST,25. 27=675