Recent Comments
benvitalis on Using Primes 2,3,5,7 only once… claudio on Using Primes 2,3,5,7 only once… David @InfinitelyMan… on Non-palindrome multiplied by i… David a/k/a @Infinit… on Integers such that √a + √b =… themusegarden on Integers such that √a + √b =…
Monthly Archives: February 2012
Powers & Permutation of Digits
Prove that the list of the numbers with the property described below is finite. I claim that you cannot find a k-digit number (k ≥ 12) with this property. N.B. There are less than 50,000 which have your property (in … Continue reading
Powers & Sum Digits – Num3ers from 2 to 99 [Part 1]
Part One: From the numbers 2 to 99 Next : Numbers from 100 to 200 I’ve checked all the numbers from 2 to 99 raised to the power k, with k = 1, 2, 3, …, 20 2^6 = 64 … Continue reading
Sum of Num3ers containing at least one 7
Find the sum of all integers from 1 to 1000 inclusive which contain at least one 7 in their digits, that is, 1 + 7 + 17 + … + 979 + 987 + 997 =
4-digit Num3ers & Reversals
8712 is an integral multiple of its reversal, 2178, as 8712 = 4 * 2178 Question: Find another 4-digit number which is a non-trivial integral multiple of its reversal.
Powers & Sum Digits [Part 2]
9^2 = 81 and 8 + 1 = 9 7^4 = 2401 and 2 + 4 + 0 + 1 = 7 8^3 = 512 and 5 + 1 + 2 = 8 17^3 … Continue reading
Numbers p; p = (p+1)^k + (p+1)^k – (p+2)^k
I’ll be looking for numbers p such that p = (p + 1)^k + (p + 1)^k – (p + 2)^k If k = 2, then p = (p + 1)^2 + (p + 1)^2 – (p + 2)^2 -p^2 … Continue reading
Numbers of the form ab * (a+b) = a^k + b^k
ab * (a+b) = a^k + b^k where ab is a 2-digit number (= 10*a + b) If k = 2, then 10 a^2 + 11 ab + b^2 = a^2 + b^2 Solution for the variable b: b = … Continue reading
Concatenation, Squares & Sums [Part 1]
(1) Of the form, AB = A || B = A^k + B^k 1,233 = 12 || 33 = 12^2 + 33^2 1000*a + 100*b + 33 = (10*a + b)^2 + 33^2 The only acceptable solutions are: a = … Continue reading
Ascending & Descending Powers
The set of these numbers is infinite. But the set of numbers that can be expressed in ascending and descending powers seems rare. The search is on! I’m particularly interested in finding prime numbers that can be expressed in sums … Continue reading
Powers are the same as the digits & the reverse
(1) Numbers where the powers are the same as the digits of the numbers 746 = 1^7 + 2^4 + 3^6 986 = 1^9 + 2^8 + 3^6 (2) Numbers where the basenumbers are the digits of the numbers For … Continue reading
