In 1970 Senge and Strauss [4] proved that the number of integers, the sum of whose digits in
each of the bases a and b lies below a fixed bound, is fmite if and only log if---is irrational …

G untzer and Paul introduced a number system with base 2 and digits 1; 0; 1 which is
characterized by separating nonzero digits by at least one zero. We nd an explicit formula …

On the Representation of Numbers as Sums of Powers of Natural Numbers Page 1 ON THE
REPRESENTATION OF NUMBERS AS SUMS OF POWERS OF NATURAL NUMBERS By RC …

We present a uniform method by which we obtain an explicit formula for the number of
representations of an integer as the sum of n squares for each n in the range 2≤ n≤ 8. The …

Four basic operations are used, ie, addition, subtraction, multiplication and division.
Numbers having potentiation are dealt separately in next section. By no means, we can say …

In this note, we introduce a novel way of doing complex arithmetic that does not involve
separating the complex numbers into their real and imaginary part~. This method uses the …

For example, the integer 564 is so representable by the three integers 122 44200
50100028778116351171 17995213613513491867,-3460 69586 84255 04865 64589 …

In 1923 GH Hardy and JE Littlewood [3] conjectured that every large integer, not being a
square, may be expressed as the sum of a prime and a square. Let v (n) be the number of …

In a recent book a statement is made for which the author says that he has no general
proof.* The statement is essentially that the average sum of the digits of integers is least …

A summation formula related to the binary digits Page 1 Invent. math. 73, 107-115 (1983)
Inventiones mathematicae 9 Springer-Verlag 1983 A Summation Formula Related to the …