:One possibility is to take this equation to be part of the " definition " of being an arithmetic progression.
42.
Fibonacci solved the congruum problem by finding a parameterized formula for generating all congrua, together with their associated arithmetic progressions.
43.
We owe him the general concept of factorial as a product of a finite number of terms in arithmetic progression.
44.
We will find three elements of { 1, . . ., 325 } in arithmetic progression that are the same color.
45.
How does one know if a sequence is an arithmetic progression given the formula for the " n " th term?
46.
:For a constructive proof, recall that an arithmetic progression looks like a + bn for some choice of a and b.
47.
Examples of approximate subgroups which are not groups are given by symmetric intervals and more generally arithmetic progressions in the integers.
48.
This theorem showed that for all sufficiently large there exist arithmetic progressions of length " n " in the prime numbers.
49.
So the evenly spaced integer topology is defined to be the topology " generated by " the family of arithmetic progressions.
50.
His early research was in number theory, investigating such topics as primes in arithmetic progression and polynomials with many initial composite values.
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