Carom 1-15
... Can we say anything about the numbers a1, a2, a3...? They will all be between 0 and 1: are some parts of (0, 1) more likely to be hit than others? ...
... Can we say anything about the numbers a1, a2, a3...? They will all be between 0 and 1: are some parts of (0, 1) more likely to be hit than others? ...
Full text
... We have received with great pleasure the announcement of the forthcoming Journal of Recreational Mathematics under the editorship of Joseph S. ...
... We have received with great pleasure the announcement of the forthcoming Journal of Recreational Mathematics under the editorship of Joseph S. ...
Pascal`s Triangle and Binomial Coefficients
... S = 2 · 2m = 2m+1 . So the sum of the entries in the (m + 1)th row also matches the theorem, and our induction is complete. Our second proof is much shorter, because it relies on the power of the binomial theorem. But the induction proof was also worth seeing, because similar ideas apply even when t ...
... S = 2 · 2m = 2m+1 . So the sum of the entries in the (m + 1)th row also matches the theorem, and our induction is complete. Our second proof is much shorter, because it relies on the power of the binomial theorem. But the induction proof was also worth seeing, because similar ideas apply even when t ...
number theory and methods of proof
... Use further methods of mathematical proof: some simple examples involving natural numbers. ...
... Use further methods of mathematical proof: some simple examples involving natural numbers. ...
Remainder Theorem
... 3) Concept of negative remainder Remainder can never be negative; its minimum value can only be 0. Consider an example of -30 / 7. Here, remainder is 5. It would not be (-28 – 2 / 7), but [(-35+5)/7] When you divide, you will get remainder of -2. Since remainder can never be negative, we subtract it ...
... 3) Concept of negative remainder Remainder can never be negative; its minimum value can only be 0. Consider an example of -30 / 7. Here, remainder is 5. It would not be (-28 – 2 / 7), but [(-35+5)/7] When you divide, you will get remainder of -2. Since remainder can never be negative, we subtract it ...
ON HIERARCHIES AND SYSTEMS OF NOTATIONS
... class) onto a family, F, of disjoint nonempty sets. The members of F may be, for example, sets of expressions, e.g. such expressions as w, uX2, w2, €o, etc. Without loss of generality we may assume that the sets in F are sets of natural numbers. We say "without loss of generality" because expression ...
... class) onto a family, F, of disjoint nonempty sets. The members of F may be, for example, sets of expressions, e.g. such expressions as w, uX2, w2, €o, etc. Without loss of generality we may assume that the sets in F are sets of natural numbers. We say "without loss of generality" because expression ...
Full text
... A Niven number is a number divisible by its digital sum. In [1] it is shown there can exist at most twenty consecutive Niven numbers; moreover, an infinite family of such is constructed where the first example requires over 4 billion digits. Here we get a lower bound on the number of digits in each ...
... A Niven number is a number divisible by its digital sum. In [1] it is shown there can exist at most twenty consecutive Niven numbers; moreover, an infinite family of such is constructed where the first example requires over 4 billion digits. Here we get a lower bound on the number of digits in each ...