(i) My house's number can be written as ABCD and it equals (A^B)*(C^D) – n, where n is the minimum with n ≥ 1. Find the number.

(ii) My cousin's house's number can be written as ABCD and it equals (A^B)*(C^D) + m, where m is the minimum with m ≥ 2. Find the number.

Note: Each of A, B, C and D denotes a digit from 0 to 9 whether same or different; A is nonzero and, at least one of C and D is nonzero. Each of m and n is an integer. ABCD denotes the concatenation of the digits.

FK, while solving "my house s number" in 2004:

"That's the only solution, though 6145 is an "off-by-1" solution (6145 = 6^1*4^5 +1). '

Now , why bother to look for "my cousin's house" number with m>1 restriction (KS's copycat version)

A SIMPLE ANSWER:  m=1 was already resolved about 8 years ago.

 

Edited on October 28, 2012, 3:50 am

Posted by Ady TZIDON on 2012-10-27 15:00:12