1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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In Hans Christian Andersen’s “The Little Mermaid” we witness that there is not an actual Heaven for the mermaid but a sub-heaven that is a reflection of Heaven. It goes to say that in “The Girl Who Stepped on Bread” also by Andersen‚ there is a sub-hell (not actual Hell)‚ where she stands in the form of a statue in the entrance hall. Both these place are not where the characters expected to be‚ yet one scarified herself ending up in a sub-heaven and the other will suffer in the entrance hall of hell
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shortage of material goods and shortage of positive external stimuli. But one thing is not lacking there: time. And time is the thing that prisoners in different ways try to shorten. For example‚ they start making journeys of the mind‚ mental journeys. What are the events and factors that caused my journey to prison? The roots of European prison literature go back a long way. In Africa‚ prison literature is much younger; this is not only because written literature there is quite recent but also because
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the battle of little bighorn is tThe Battle of the Little Big Horn ensured for General George Custer the fame he had always wanted. His death and the destruction of those men in the US Army’s Seventh Cavalry who fought with him by the largest gathering of Native American warriors that the country had seen‚ immortalised Custer in films‚ books and in the psyche of Americans. Paintings by the likes of Edgar Paxson and Kurz and Allison portrayed Custer as the all-American hero fighting with his men to
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What So Funny? A humorous story is a comedy. A serious story is a drama. Put both of these kinds of stories together and you get Flannery O’Connor’s writing style. O’Connor’s short stories begin with an up beat tone‚ and then slowly trickle into a more serious‚ dramatical tone. This style of writing is what helped O’Connor’s stories stick in our minds from her death until now. Her short stories "A Good Man is Hard to Find"‚ "Revelation"‚ and "Good Country People" are good examples of her writing
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"Abnormality of Stuart" In Raymond Carver’s "So Much Water So Close to Home"‚ Carver exposes to the reader that Stuart has some emotional problems. Sudden outbursts and verbal eruptions are not uncommon for Stuart‚ as he continuously yells at his wife throughout the story. From this I am able to infer that Stuart has a dual personality‚ one side being normal and the other as a disturbed person. In this analysis of Stuart‚ I am going to show that by the following textual clues that he is not
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numerous reasons. One reason for this is all the beautiful attractions the "Little Grand Canyon" offers to people. In the first paragraph‚ it says‚ "Travelers who visit the forested areas near Lumpkin‚ Georgia‚ often think they have made a few wrong turns and have ended up in America’s southwest instead of Georgia’s southwest. That’s because of the beautiful sandstone formations found in an area nicknamed Georgia’s "Little Grand Canyon." As you can see this is explaining that people have argued over
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From the beginning of Rock n’ Roll in the 50’s‚ till’ the now ever growing present generation of Rock n’ Roll‚ there have been many famous musicians. But there are only a few who can be said to be the kings of Rock n’ Roll. Little Richard‚self proclaimed the “Architect of Rock n’ Roll”‚ was one of the most energetic and enthusiastic Rock n’ Roll musicians there is to date.Little Richard is the true king of Rock n’ Roll because of the way he portrayed himself through a troubling new era.His attitude
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looking for a quick‚ entertaining and juicy read‚ the Pretty Little Liars series could be a good companion for a rainy afternoon. We won’t be chattin’ philosophy‚ science or complex issues by the close of the final (cliffhanger of a) page‚ but that’s not what this is all about. This was cotton candy: fluffy and fun. And with six additional books in Shepard’s series‚ there’s plenty more where this snack of a story came from.Pretty Little Liars is a series of young-adult novels by author Sara Shepard
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The classic folk tale‚ Three Little Pigs‚ provides many opportunities for fun learning activities across the curriculum. Here are some suggestions. Three’s the Charm Focus on the number three. Read other stories‚ such as Three Billy Goats Gruff and Goldilocks and the Three Bears‚ or recite a rhyme such as Three Little Kittens. Have each child draw a picture of three of the same thing. Label each drawing: 3 chairs‚ 3 bears‚ 3 flowers‚ etc. Gather the illustrations into a class book about the number
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