I have problem solving this equation, smallest n such that $1355297$ divides $10^{6n+5}-54n-46$. I tried everything using my scientific calculator, but I never got the correct results(!).and finally I gave up!. Could you help me find the first 2 solutions for this equation ? (thanks.)
Answer
$n_1 = 2331259$, $n_2 = 3776127$,
Obtained from this Mathematica code:
cf = Compile[{{m, _Integer}},
Block[{n, a, b, p, counter = 0,result},
result = ConstantArray[0, m];
p = 1355297;
n = 0;
a = Mod[10^(5), p];
b = 0;
While[counter < m,
n++;
a = Mod[a 1000000, p];
b = Mod[b - 54 , p];
While[Mod[a + b - 46, 1355297] != 0,
n++;
a = Mod[a 1000000, p];
b = Mod[b - 54 , p];
];
counter++;
result[[counter]] = n;
];
result
],
CompilationTarget -> "C"
];
cf[2]
{2331259, 3776127}
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