The length of the three sides of a triangle are positive integers A, B and C, with A < B < C and satisfying:
{3^{A}/10^{4}}= {3^{B}/10^{4}}= {3^{C}/10^{4}}
where, {x}=x[x] and, [x] denotes the greatest integer ≤ x
Determine the minimum perimeter length of the triangle.
(In reply to
re: possible solution. by Ady TZIDON)
Ady, you are quite right, the divisor is 10^4, not 10^3.
Using the same method, and given the period (500) for the last 4 digits of 3^n, by analogy the minimum perimeter = 3003.
For obvious reasons, ascertainment of the last 4 digits does not require direct calculation.
Edited on September 20, 2013, 3:57 pm

Posted by broll
on 20130920 15:42:21 