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Home » So for each pair, 30 valid sequences. - Imagemakers

So for each pair, 30 valid sequences. - Imagemakers

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Try $ d = 10 $: $ x + y = 100 $, many such pairs.

📌 Try $ d = 5 $: $ x + y = 200 $, many such pairs.

📌 Try $ d = 4 $: $ x + y = 250 $, many such pairs.

📌 Try $ d = 2 $: $ x + y = 500 $, many such pairs.

📌 Try $ d = 1 $: $ x + y = 1000 $, many such pairs.

📌 Question: How many of the 100 smallest positive integers are congruent to 2 modulo 7?

📌 Such numbers are of the form $ n = 7k + 2 $.

📌 Question: What is the remainder when $ 11071 + 11073 + 11075 + 11077 $ is divided by 12?

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