Determine the total number of positive integers
T ≥ 2, for which the relationship:
Y25 ≡ Y (mod T) holds true for all possible values of a positive integer
Y ≥ 2, where the "≡" symbol denotes
congruence.
As 2^25 = 33,554,432, T greater than this value need not be tested as those modular results for this power of 2 would not reduce it to 2.
The following program tests T up to 34,000,000. (Variable I was used in place of Y):
10 for T=2 to 34000000
20 Good=1
30 for I=1 to T-1
40 if (I^25)@T<>I then Good=0:cancel for:goto 100
50 next
100 if Good then print T;:Ct=Ct+1
150 next T
200 print:print Ct
It found 31 values of T:
2 3 5 6 7 10 13 14 15 21 26 30 35 39 42 65 70 78 91 105 130 182 195 210 273 390 455 546 910 1365 2730
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Posted by Charlie
on 2008-10-30 11:10:06 |
computer solution (spoiler)
