Thứ Hai, 7 tháng 1, 2019

IMO 1959- Problem 1

Problem: For every integer $n$ prove that the fraction $\frac{21n+4}{14n+3}$ cannot be reduced any further.
Solution: The desired result $(14n+3,21n+4)=1$ follows from $3(14n+3)-2(21n+4)=1$.
vào lúc
Nhãn:

Không có nhận xét nào:

Đăng nhận xét

Đăng ký: Đăng Nhận xét (Atom)

IMO 1964 - Problem 6

Problem: Given a tetrahedron ABCD, let D1 be the centroid ò the triangle ABC and let A1,B1,C1 be the intersection points of the lines paral...

  • IMO 1994- Problem 3
    Problem: For any positive integer $k$, let $f(k)$ be the number of elements in the set $\left\{k+1,k+2,...,2k\right\}$ whose base $2$ repre...
  • IMO 1964 - Problem 3
    Problem: The circle is inscribed in a triangle $ABC$ with sides $a,b,c$. Three tangents to the incircle are drawn, each of which is paralle...
  • IMO 1960 - Problem 1
    Problem: Find all the three-digit numbers for which one obtains, when dividing the number by $11$, the sum of squares of the digits of the ...