Toán Olympic quốc tế 2002 Tiếng Anh
Toán Olympic quốc tế 2002 Tiếng Anh
... Starting with2002 2002 2002 = 10 3 + 10 3 + 1 3 + 1 3 and using once again, we find that2002 = 667 × 3 + 1 2002 2002 = 2002 × ( 2002 667 ) 3 = ( 10 × 2002 667 ) 3 + ( 10 × 2002 667 ) 3 + ( 2002 667 ) 3 + ( 2002 667 ) 3 . Comments 1. ... x 3 2 + … +x 3 t = 2002 2002 ? Solution. The answer is .t = 4 We first show that is not a sum of three cubes by considering numbers modulo...
Ngày tải lên: 05/04/2014, 00:14
Toán Olympic quốc tế 2003 Tiếng Anh
... contains the centre O of the disc S. Therefore the number of such discs is less than or equal to 2002. We will show that if a disc D k has its centre inside T i and intersects S, then D k contains P i , ... equal to 2003. Consequently, the number of discs D k that intersect S is less than or equal to 2002 + 6 · 2003 = 7 · 2003 − 1.
Ngày tải lên: 05/04/2014, 00:14
