.
The given number has 2 + 3*5 = 17 digits - hence, the unknown integer is less than 10. So, it is one-digit number.
In addition, it is an odd number.
There is no need to explain that it can not be 1.
Hence, it can be one of the "3", "5", "7" or "9" only.
The "5" can produce only 5 as the last digit.
The "7" produces the last digits 7, 9, 3, 1, 7 . . . cyclically; so the 35-th degree must have the last digit 3.
Thus, "7" does not work.
The "9" produces the last digits 9, 1, 9, 1, . . . cyclically and never produces 7 as the last digit.
As a conclusion, only "3" can be that number under the question.
ANSWER. 3.
