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42. Prove that there exists an increasing infinite sequence of triangular
numbers (i.e. numbers of the form tn = -1/2 n(n+ 1), n = 1, 2, ... ) such that
every two of them are relatively prime.
41. Prove that for every integer k the numbers 2k+1 and 9k+4 are rel-
atively prime, and for numbers 2k-1 and 9k+4 find their greatest common
divisor as a function of k.
The number of traffic violation recorded by police department for 10 day period is given. Calculate the first quartile, second quartile, third quartile and inter quartile range.
22 19 25 24 18 15 9 12 16 20
5 m wire made of gold ( ρgold = 2.4 x 10−8 ) has a cross-sectional area of 2 mm.
Calculate the voltage if a 32 A current runs through the wire.
5. Prove that "19|2^{2^{6k+2}}+3" for k = 0, 1, 2, ....
4. Prove that for positive integer n we have 169|33n+3-26n-27.
3. Prove that there exists infinitely many positive integers n such that 4n2+ 1 is divisible both by 5 and 13.
2. Find all integers x #= 3 such that x-3Ix3-3.
1. Find all positive integers n such that n2+ 1 is divisible by n+ 1.
Name a non-polyhedral and say why it cannot be a platonic solid
