# Find the divisors

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Let $n$ be the least positive integer for which $149^n-2^n$ is divisible by $3^3\cdot5^5\cdot7^7.$ Find the number of positive integer divisors of n

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Lifting the Exponent shows that

so thus,  divides . It also shows that

so thus,  divides .

Now, multiplying  by , we see

and since  and  then  meaning that we have that by LTE,  divides .

Since  and  all divide , the smallest value of  working is their LCM, also . Thus the number of divisors is .