Full text
... Let Dn denote the determinant of An , and sn = x0 + x1 + · · · + xn−1 . Prove that if the xk ’s are integers such that sn 6= 0, then sn |Dn . Solution by H.-J. Seiffert, Berlin, Germany Adding the second, third, fourth, . . . and last row to the first row in Dn , we arrive to the determinant En , wh ...
... Let Dn denote the determinant of An , and sn = x0 + x1 + · · · + xn−1 . Prove that if the xk ’s are integers such that sn 6= 0, then sn |Dn . Solution by H.-J. Seiffert, Berlin, Germany Adding the second, third, fourth, . . . and last row to the first row in Dn , we arrive to the determinant En , wh ...
Full text
... (mod pn ) implies ap−1 ≡ 1 (mod pn ). This shows that there are in fact infinitely many primes a satisfying the given condition (by Dirichlet’s Theorem). For other solutions, observe that since the multiplicative group (Z/pn Z)× of units of Z/pn Z has order φ(pn ) = pn−1 (p − 1), n−1 we get that (bp ...
... (mod pn ) implies ap−1 ≡ 1 (mod pn ). This shows that there are in fact infinitely many primes a satisfying the given condition (by Dirichlet’s Theorem). For other solutions, observe that since the multiplicative group (Z/pn Z)× of units of Z/pn Z has order φ(pn ) = pn−1 (p − 1), n−1 we get that (bp ...
Slide 1
... In your notebook, answer the following question. Sally Sue just received her cable bill from Comcast. The bill for the month is a total of $114.50. Comcast charges $5.00 for each movie ordered “On Demand.” Sally Sue can’t remember how many “On Demand” movies she ordered in the month? If Sally Su ...
... In your notebook, answer the following question. Sally Sue just received her cable bill from Comcast. The bill for the month is a total of $114.50. Comcast charges $5.00 for each movie ordered “On Demand.” Sally Sue can’t remember how many “On Demand” movies she ordered in the month? If Sally Su ...
Homework Text page 117, #1
... To add two integers with the SAME signs, find the sum of their absolute values. Use the sign of the two integers ...
... To add two integers with the SAME signs, find the sum of their absolute values. Use the sign of the two integers ...
Full text
... believed to be new or extending old results. Proposers should submit solutions or other information that will assist the editor. To facilitate their consideration, solutions should be submitted on separate signed sheets within two months after publication of the problems. H-239 Proposed by D. Finkel ...
... believed to be new or extending old results. Proposers should submit solutions or other information that will assist the editor. To facilitate their consideration, solutions should be submitted on separate signed sheets within two months after publication of the problems. H-239 Proposed by D. Finkel ...
