Search found 2 matches

by umme.habiba.lamia
Mon Dec 04, 2017 1:09 pm
Forum: Junior Level
Topic: The Chinese Remainder Theorem
Replies: 1
Views: 462

The Chinese Remainder Theorem

Consider the following simultaneous congruence. x=3 (mod II), x = 5 (mod 6). It is easy to find a solution, x = 47, by inspection. Here's another method. Since 61-II, we can find a linear combination of 6 and II that equals one, for example, ( -I) . II + 2·6 = I. Now compute 5·(-1)·11 +3·2·6= -19. T...
by umme.habiba.lamia
Mon Dec 04, 2017 1:04 pm
Forum: Junior Level
Topic: IMO 1975
Replies: 2
Views: 581

IMO 1975

Let f(n) denote the sum of the digits of n. (a) For any integer n, prove that eventually the se quence f(n),f(f(n) ),f(f(f(n))), . . . will become constant. This constant value is called the digital sum of n. (b) Prove that the digital sum of the product of any two twin primes, other than 3 and 5, i...