A Fermat number is a of the form , where n an integer 0. composite (see Dickson [1] or Hardy and Wright [2] Ikorong [3]) non-prime prime number. composites primes are char­acterized via divisibility in [3] [4]. It known that for every j ∈ {0, 1, 2, 3, 4}, Fj it also Paul [5]) F5 F6 641×6700417, since 2013, +1 number). In this paper, we show [via elementary arithmetic congruences] following Resu...

Abstract Analogously to primes in arithmetic progressions large moduli, we can study that are totally split extensions of ${\mathbb {Q}}$ high degree. Motivated by a question Kowalski focus on the {Q}}(E[d])$ obtained adjoining coordinates $d$-torsion points non-CM elliptic curve $E/{\mathbb {Q}}$. We show for almost all integers $d$ there exists and prime $p<|\text {Gal}({\mathbb {Q}}(E...

Buchmann and Pethő [5] observed that following algebraic integer 10 + 9α + 8α + 7α + 6α + 5α + 4α, with α = 3 is a unit. Since the coefficients form an arithmetic progressions they have found a solution to the Diophantine equation (1) NK/Q(x0 + αx1 + · · ·+ x6α) = ±1, such that (x0, . . . , x6) ∈ Z is an arithmetic progression. Recently Bérczes and Pethő [3] considered the Diophantine equation ...

The purpose of this study is to explain the doctrine expectations learning mathematics. Data was collected through testing, interviews, and documentation. Researchers have designed a virtual trajectory (HLT) based on examining obstacles students face when Next, didactic design developed from HLT. method implemented, results showed that situation three principles expected by researchers scaffold...

Children's arithmetical difficulties are often explained in terms of a short-term memory deficit. However, the underlying cause of this memory deficit is unclear, with some researchers suggesting a slow articulation rate and hence increased decay of information during recall, while others offer an explanation in terms of slow speed of item identification, indicating difficulty in retrieving inf...

We present a term rewriting system for interval arithmetic (addition, subtraction and multiplication), toward a mathematical model for interval computation. We start presenting a term rewriting system whose rules (directed equations) perform binary floating-point arithmetic, which is based on IEEE-754 Standard. Next, this primitive system is extended with rules for interval arithmetic. Finally,...

The approximate number system (ANS) is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-min training sessi...