MathDB

20

Part of 2020 BMT Fall

Problems(2)

integer ABCD, AB=AD, BC=CD, <ABC=<BCD=<CDA 2020 BMT Team 20

Source:

1/7/2022
Non-degenerate quadrilateral ABCDABCD with AB=ADAB = AD and BC=CDBC = CD has integer side lengths, and ∠ABC=∠BCD=∠CDA\angle ABC = \angle BCD = \angle CDA. If AB=3AB = 3 and B≠DB \ne D, how many possible lengths are there for BCBC?
geometryequal segmentsequal angles
2020 BMT Individual 20

Source:

1/9/2022
Compute the number of positive integers n≤1890n \le 1890 such that n leaves an odd remainder when divided by all of 2,3,52, 3, 5, and 77.
number theory