The number 5353714662021596247595065017236556037762353639503 is the nineteenth power of a positive integer.

Find the integer using just pen and paper.

(In reply to

An analytic start and a calculator finish by Charlie)

All I know without calculator :

1. N is a 3-digit number, between 300 and 400.

2. The units digit of N is **7** (7931 being the cycle, 3 is in 19th place)

So the number is **3?7 - **to find "**?**" - few calculators trials.

... Who called it a **p&p** problem?