Arithmetic of the modular function $j_{1,4}$
نویسندگان
چکیده
منابع مشابه
Modular arithmetic
Since congruence modulo m is an equivalence relation, it partitions the universe of integers into equivalence classes, which we’ll call congruence classes modulo m. Within any one of these classes, all of the members are congruent to all of the other members; but congruence modulo m never holds between members of different equivalence classes. For instance, there are two congruence classes modu...
متن کاملOrders in Modular Arithmetic
Example 1.1. Let m = 7. The following table shows that the first time a nonzero number mod 7 has a power congruent to 1 varies. While Fermat’s little theorem tells us that a6 ≡ 1 mod 7 for a 6≡ 0 mod 7, we see in the table that the exponent 6 can be replaced by a smaller positive exponent for 1, 2, 4, and 6. k 1 2 3 4 5 6 1k mod 7 1 2k mod 7 2 4 1 3k mod 7 3 2 6 4 5 1 4k mod 7 4 2 1 5k mod 7 5 ...
متن کاملModular Arithmetic Decision Procedure
All integer data types in programs (such as int, short, byte) have an underlying finite representation in hardware. This finiteness can result in subtle integer-overflow errors that are hard to reason about both for humans and analysis tools alike. As a first step towards finding such errors automatically, we will describe two modular arithmetic decision procedures for reasoning about bounded i...
متن کاملModular Curves and Arithmetic
for relatively prime integers a and N, generate subgroups of finite index in the group of units of number fields F which are abelian over Q. The interest in circular units stems from the fact that theyare "sufficiently many" explicitly constructed units, and also from the fact that their "position" in the full group of global units (and in certain groups of local units) bears upon deep arithmet...
متن کاملOptical modular arithmetic
Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary “selector” vector, where the arithm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1998
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-84-2-129-143