of 616 and 32 3. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q‚ 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.] 4. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m‚ 9m + 1 or 9m + 8. 5. Consider the numbers 4n‚ where n is a natural number
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First Day at School in a New Country My family moved to the United States when I was fourteen‚ and I learned I would be going to a new school just two days after we had entered the country and I wasn’t assimilated to the culture or the language. Even though I took lots of English lessons when I was in China‚ when I learned I would not be attending a bilingual school like the other new immigrants‚ I was extremely apprehensive. My first day of school in a new country was extremely nervous
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A day I will always remember is the first day of middle school‚ which was the first day of 6th grade. I was nervous and didn’t know what to expect‚ but I was also very excited at the same time. Everything was so new to me‚ the campus‚ the schedule‚ and the people. But the first day of middle school will always be a day I will remember. It was the first day of the 6th Grade and I was very anxious. I had been waiting for that day all summer. It all started when I got of the school bus. The
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My First Day In The U.S. As I remember it‚ the first day that I came to U.S. was June 26‚ 2006. My first day in U.S. was both exciting and upsetting‚ I was exciting about was seeing my mom for the first time over a year‚ the upsetting part is I had to leave my good memories in my hometown. I had to left all of that behind friends‚ family and schools. However‚ life moves on‚ things need to be done. When I got out of the terminal in LAX‚ I saw the smile on my mother’s face that was the happiest
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In India‚ Republic Day honors the date on which the Constitution of India came into force replacing the Government of India Act 1935 as the governing document of India on 26 January 1950. The date of 26 January was chosen to honour the declaration of independence of 1930. It is one of the three national holidays in India. While the main parade takes place in the national capital‚ New Delhi‚ at the Rajpath before the President of India (currently Pranab Mukherjee)‚ the anniversary is also celebrated
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Friendship / Friend quotes‚ Friendship / Friends Poem and always keep searching for a heart touching Best Friend Quote‚urdu or hindi friendship sms or Fest Friend Poem to pickup and send to our friends. Friendship day is celebrated on the first sunday of August every year‚ so the upcoming Friendship day 2012 is on August 5 2012. You may wish to celebrate & send out tons of friendship sms / friendship text messages to your best friends as well as old forgotton friends. Here we have gathered a nice collection
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"The Longest Day" was a mammoth project dramatizing D-day‚ the Allied invasion of France. It was nearly three hours in length and with an enormous ensemble cast‚ all playing supporting roles. The production was very conscientious about realism‚ the actors were always of the same nationality as their characters‚ and spoke in their native languages‚ leading to a lot of subtitles translating French and German dialogue. Although the movie was historically correct‚ it was also meant to be a blockbuster
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Personal Essay Something so tragic couldn’t have happened on the best day of my life‚ "My Graduation Day." The day itself had actually been going very well indeed‚ and a seemingly endless surge of excitement had me going crazy! Things were going perfectly how I imagined it‚ I have been waiting for this day for 12 long years and just knowing the fact that it was here just drove me insane. The morning started out when I woke up and had a wonderful breakfast waiting for me out on the table with my
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Teachers’ Day is celebrated on the 5th of September‚ the birth anniversary of my pre-eminent predecessor‚ Dr Sarvepalli Radhakrishnan‚ who was one of the great scholars and philosophers of our country. When he became the President of India in 1962‚ his admirers requested him to allow them to celebrate his birthday. Dr Radhakrishnan‚ who himself was an accomplished teacher‚ said‚ "instead of celebrating my birthday separately‚ it would be my proud privilege if the 5th of September
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Clara’s day This short story "Clara’s day" by Penelope Lively is about a girl‚ Clara‚ who suddenly took off all of her clothes and started walking naked around at her school. After this sensational episode she was told that she had to meet "the Head" after school. They talked about Clara’s reasons for doing what she did‚ because as the Head said on page 53 line 1-2‚ "..you aren’t really like that‚ are you?"‚ and Clara agreed that she wasn’t. Naturally Clara’s parents‚ or in this case‚ mother was
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