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The elementary charge e, i.e. the negative charge on a single electron or the positive charge on a single proton [3] 10 −18: atto-(aC) ~ 1.8755 × 10 −18 C: Planck charge [4] [5] 10 −17: 1.473 × 10 −17 C (92 e) – Positive charge on a uranium nucleus (derived: 92 x 1.602 × 10 −19 C) 10 −16: 1.344 × 10 −16 C: Charge on a dust ...
Even without knowledge that we are working in the multiplicative group of integers modulo n, we can show that a actually has an order by noting that the powers of a can only take a finite number of different values modulo n, so according to the pigeonhole principle there must be two powers, say s and t and without loss of generality s > t, such that a s ≡ a t (mod n).
The group (/) is cyclic if and only if n is 1, 2, 4, p k or 2p k, where p is an odd prime and k > 0. For all other values of n the group is not cyclic. [ 1 ] [ 2 ] [ 3 ] This was first proved by Gauss .
The anti-personnel obstacle breaching system (APOBS) is an explosive line charge system that allows safe breaching through complex antipersonnel obstacles, particularly fields of land mines. The APOBS is a joint DOD program for the U.S. Army and the United States Marine Corps.
The constants R mod N and R 3 mod N can be generated as REDC(R 2 mod N) and as REDC((R 2 mod N)(R 2 mod N)). The fundamental operation is to compute REDC of a product. When standalone REDC is needed, it can be computed as REDC of a product with 1 mod N. The only place where a direct reduction modulo N is necessary is in the precomputation of R ...
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
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c ≡ 4 13 (mod 497) One could use a calculator to compute 4 13; this comes out to 67,108,864. Taking this value modulo 497, the answer c is determined to be 445.