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Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

12 votes
8 answers
2k views

Find the minimum integer r such that $(10^r - 1)/37$ is an integer

I know Element[(10^r - 1)/37, Integers] tests the condition. So what is the command that gives me the minimum integer value r such that the condition is true?
Gqqnbig's user avatar
  • 307
1 vote
0 answers
82 views

Input `Reduce[Mod[a + x, l] == 0, x]' and output `x == -a + kl`?

Reduce[a + x == k l && k > 0, x] (* k > 0 && x == -a + k l *) I think a + x == k l and Mod[a + x, l] == 0 are equivalent, but when I replace a + x == k l by Mod, Mathematica can't produce the previo …
Gqqnbig's user avatar
  • 307