OPEN DIOPHANTINE PROBLEMS 1. Diophantine Equations 1.1
... Our goal here is not to describe in detail the state of the art regarding these questions (see for instance [La8]). It suffices to say – that a complete answer to question (a) is not yet available. There is no algorithm (not even a conjectural one) to decide whether a curve has a rational point or n ...
... Our goal here is not to describe in detail the state of the art regarding these questions (see for instance [La8]). It suffices to say – that a complete answer to question (a) is not yet available. There is no algorithm (not even a conjectural one) to decide whether a curve has a rational point or n ...
Arithmetic Series I
... Sequence A, B and C all have the same first term but a different a20. They all also contain the number 200, but this occurs the earliest in A. Therefore, A must have the largest common difference and the largest a20 (≈ 300). Sequence D and E both have a larger first term than A, but they are both de ...
... Sequence A, B and C all have the same first term but a different a20. They all also contain the number 200, but this occurs the earliest in A. Therefore, A must have the largest common difference and the largest a20 (≈ 300). Sequence D and E both have a larger first term than A, but they are both de ...
Full text
... Several conclusions are immediate from Theorem 2. By (a), 0 and g/2 are not contained in an F-cycle. Moreover, (g) is an F-cycle of length 1. This cycle is called the trivial cycle; all other cycles are proper cycles. Part (b) tells us that proper cycles exist if and only if g is not a power of 2. B ...
... Several conclusions are immediate from Theorem 2. By (a), 0 and g/2 are not contained in an F-cycle. Moreover, (g) is an F-cycle of length 1. This cycle is called the trivial cycle; all other cycles are proper cycles. Part (b) tells us that proper cycles exist if and only if g is not a power of 2. B ...
Document
... 4-9 Multiplying Fractions by Whole Numbers Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method. ...
... 4-9 Multiplying Fractions by Whole Numbers Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method. ...
Full text
... for distinct odd primes p, ql9 ..., qt, with p = a = 1 (mod 4). (We shall always assume this form for the prime factor decomposition of N) . Many writers have found conditions which must be satisfied by the exponents 23i» ...5 2(3t» and it is our intention here to extend some of those results. We sh ...
... for distinct odd primes p, ql9 ..., qt, with p = a = 1 (mod 4). (We shall always assume this form for the prime factor decomposition of N) . Many writers have found conditions which must be satisfied by the exponents 23i» ...5 2(3t» and it is our intention here to extend some of those results. We sh ...
Did I get it right? COS 326 Andrew W. Appel Princeton University
... – Eg: When proving a theorem about natural numbers by induction, and considering the case for natural number k+1, we get to assume our theorem is true for natural number k (because k is smaller than k+1) – Eg: When proving a theorem about lists by induction, and considering the case for a list x::xs ...
... – Eg: When proving a theorem about natural numbers by induction, and considering the case for natural number k+1, we get to assume our theorem is true for natural number k (because k is smaller than k+1) – Eg: When proving a theorem about lists by induction, and considering the case for a list x::xs ...
Higher Student Book Chapter 2
... You can use the nth term of an arithmetic sequence to generate the terms of a sequence. You can use the terms of a sequence to find out whether or not a given number is part of a sequence, and ...
... You can use the nth term of an arithmetic sequence to generate the terms of a sequence. You can use the terms of a sequence to find out whether or not a given number is part of a sequence, and ...
- Towngate Primary Academy
... Recall and use multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables (through doubling, connect the 2, 4 and 8s). Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit num ...
... Recall and use multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables (through doubling, connect the 2, 4 and 8s). Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit num ...
Searching for Large Elite Primes
... that their number is finite. For further open problems on Fermat numbers see Richard Guy’s famous book [Guy 04]. We call a prime number p elite if there is an integer index m for which all Fn with n > m are quadratic nonresidues modulo p, i.e., there is no solution to the congruence x2 ≡ Fn mod p for ...
... that their number is finite. For further open problems on Fermat numbers see Richard Guy’s famous book [Guy 04]. We call a prime number p elite if there is an integer index m for which all Fn with n > m are quadratic nonresidues modulo p, i.e., there is no solution to the congruence x2 ≡ Fn mod p for ...
Radicals Working with Exponents
... contains an odd number of twos? If so, find the integer. If not, explain why. 4. Follow these steps. • Choose an integer b. • Square the integer. • Multiply the squared integer by 2. • Find the prime factorization of the result. How many twos are in the prime factorization? Repeat this process with ...
... contains an odd number of twos? If so, find the integer. If not, explain why. 4. Follow these steps. • Choose an integer b. • Square the integer. • Multiply the squared integer by 2. • Find the prime factorization of the result. How many twos are in the prime factorization? Repeat this process with ...
