... There are infinitely many exceptions to Khinchin’s Claim, and only finitely many non-exceptions, none of which conclusive. The Modern Circle Squarers cannot let go of Khinchin’s Claim and made any number that violates it into an exception. It is safe to say that Khinchin Claim allows for most except ...
6 The Congruent Number Problem FACULTY FEATURE ARTICLE
... as the area of a rational right triangle. For instance, no rational right triangle has area 1. This was proved by Fermat. The question we will examine here is: which rational numbers occur as the area of a rational right triangle? Definition 1. A positive rational number n is called a congruent numb ...
... as the area of a rational right triangle. For instance, no rational right triangle has area 1. This was proved by Fermat. The question we will examine here is: which rational numbers occur as the area of a rational right triangle? Definition 1. A positive rational number n is called a congruent numb ...
x - El Camino College
... • If we divide P(x) by x – b (with b > 0) using synthetic division, and if the row that contains the quotient and remainder has no negative entry, then b is an upper bound for the real zeros of P. • If we divide P(x) by x – a (with a < 0) using synthetic division, and if the row that contains the qu ...
... • If we divide P(x) by x – b (with b > 0) using synthetic division, and if the row that contains the quotient and remainder has no negative entry, then b is an upper bound for the real zeros of P. • If we divide P(x) by x – a (with a < 0) using synthetic division, and if the row that contains the qu ...
INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS
... and large enough x, the count exceeds x2/7 , and under a weaker hypothesis there are infinitely many elliptic Carmichael numbers. Both of these hypotheses are bounds on the least prime in arithmetic progressions and are weaker than the conjectured bound, recalled below. In addition, under the same h ...
... and large enough x, the count exceeds x2/7 , and under a weaker hypothesis there are infinitely many elliptic Carmichael numbers. Both of these hypotheses are bounds on the least prime in arithmetic progressions and are weaker than the conjectured bound, recalled below. In addition, under the same h ...
Recreational Mathematics - FAU Math
... 1.2 Counting primitive triangles We shall make use of the famous Euler polyhedron formula. Theorem 1.2. If a closed polyhedron has V vertices, E edges and F faces, then V − E + F = 2. Given a lattice polygon with a partition into primitive lattice triangles, we take two identical copies and glue the ...
... 1.2 Counting primitive triangles We shall make use of the famous Euler polyhedron formula. Theorem 1.2. If a closed polyhedron has V vertices, E edges and F faces, then V − E + F = 2. Given a lattice polygon with a partition into primitive lattice triangles, we take two identical copies and glue the ...
(pdf)
... where the pi are distinct primes. Let’s first do the case where there are at least two different primes in this product, i.e. r > 1. Because ei × pi ≤ pei i < M , (M − 1)! contains all the numbers p1 , 2p1 , 3p1 , . . . , ei pi as factors, so that pei i |(M − 1)!. Since this is true for any i, it fo ...
... where the pi are distinct primes. Let’s first do the case where there are at least two different primes in this product, i.e. r > 1. Because ei × pi ≤ pei i < M , (M − 1)! contains all the numbers p1 , 2p1 , 3p1 , . . . , ei pi as factors, so that pei i |(M − 1)!. Since this is true for any i, it fo ...
Full text
... Note that given an escalator number A = An , for each m > n, the values of am and Am are completely determined. We now investigate the degree to which these values are determined for m ≤ n. Let a1 , a2 , a3 , a4 , . . . be an escalator sequence. Since A2 = a1 + a2 = a1 a2 , it’s also true that A2 = ...
... Note that given an escalator number A = An , for each m > n, the values of am and Am are completely determined. We now investigate the degree to which these values are determined for m ≤ n. Let a1 , a2 , a3 , a4 , . . . be an escalator sequence. Since A2 = a1 + a2 = a1 a2 , it’s also true that A2 = ...