MathDB

12

Part of 2017 Hanoi Open Mathematics Competitions

Problems(2)

2017 consecutive integers with 17 primes (HOMC 2017 J Q12)

Source:

8/7/2019
Does there exist a sequence of 20172017 consecutive integers which contains exactly 1717 primes?
number theoryconsecutive integersprimes
length of NM depends on position of C? (HOMC 2017 Q12)

Source:

8/3/2019
Let (O)(O) denote a circle with a chord ABAB, and let WW be the midpoint of the minor arc ABAB. Let CC stand for an arbitrary point on the major arc ABAB. The tangent to the circle (O)(O) at CC meets the tangents at AA and BB at points XX and YY, respectively. The lines WXW X and WYW Y meet ABAB at points NN and MM , respectively. Does the length of segment NMNM depend on position of CC ?
fixedgeometrySegment