On a sequence of prime numbers
... whence adding the congruences we have kie = 1 (mod 2) and the assertion. Theorem 1 provides a sufficient condition for the non-occurrence of a prime; further, if the condition excludes a prime it also excludes all smaller primes which have not already occurred. Hence it excludes the smallest N prime ...
... whence adding the congruences we have kie = 1 (mod 2) and the assertion. Theorem 1 provides a sufficient condition for the non-occurrence of a prime; further, if the condition excludes a prime it also excludes all smaller primes which have not already occurred. Hence it excludes the smallest N prime ...
LOWNESS NOTIONS, MEASURE AND DOMINATION
... u.a.e. domination and p.m. domination for the reverse mathematics question of how difficult it is to prove that POS → Gδ -REG. In Section 5, we show that RCA0 is not strong enough to prove this implication, or even that Gδ -ε → Gδ -REG. In Section 7, we show that WWKL0 ` POS → Gδ -REG. Notice that s ...
... u.a.e. domination and p.m. domination for the reverse mathematics question of how difficult it is to prove that POS → Gδ -REG. In Section 5, we show that RCA0 is not strong enough to prove this implication, or even that Gδ -ε → Gδ -REG. In Section 7, we show that WWKL0 ` POS → Gδ -REG. Notice that s ...
Transcendence of Various Infinite Series Applications of Baker’s Theorem and
... I would first like to thank Professor M. Ram Murty for his wisdom and helpfulness. His guidance kept this research on track keeping things both interesting and enjoyable. I would also like to thank David Wehlau, Mike Roth, Ernst Kani, and Ole Nielsen from Queen’s University and Margaret Beattie from ...
... I would first like to thank Professor M. Ram Murty for his wisdom and helpfulness. His guidance kept this research on track keeping things both interesting and enjoyable. I would also like to thank David Wehlau, Mike Roth, Ernst Kani, and Ole Nielsen from Queen’s University and Margaret Beattie from ...
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... Given an integer n and the subsets of its proper divisors di |n and di < n (thus 0 < i < τ (n) where τ is the divisor function), is there at least one subset whose elements add up to n? If yes, then n is a semiperfect number or pseudoperfect number. Since the complete set of proper divisors is also ...
... Given an integer n and the subsets of its proper divisors di |n and di < n (thus 0 < i < τ (n) where τ is the divisor function), is there at least one subset whose elements add up to n? If yes, then n is a semiperfect number or pseudoperfect number. Since the complete set of proper divisors is also ...
Full text
... The authors define the notion of an independent Pythagorean number and they prove that there exist infinitely many primitive Pythagorean numbers that are not independent (Theorem 10, p. 40). According to that definition (Definition 2, p. 40), a Pythagorean number is called independent if it cannot b ...
... The authors define the notion of an independent Pythagorean number and they prove that there exist infinitely many primitive Pythagorean numbers that are not independent (Theorem 10, p. 40). According to that definition (Definition 2, p. 40), a Pythagorean number is called independent if it cannot b ...
