Solution to the Problem:
There are three solutions to the cryptarithm:
ELVIS * A + PRESLEY + 1935 + 1977 + P = PPPPPPP
19750 * 6 + 3210918 + 1935 + 1977 + 3 = 3333333
73268 * 1 + 5478370 + 1935 + 1977 + 5 = 5555555
82495 * 7 + 6085283 + 1935 + 1977 + 6 = 6666666
In the first solution, here are the values of the letters:
E L V I S A P R Y
1 9 7 5 0 6 3 2 8
In the second solution, here are the values of the letters:
E L V I S A P R Y
7 3 2 6 8 1 5 4 0
In the third solution, here are the values of the letters:
E L V I S A P R Y
8 2 4 9 5 7 6 0 3