Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 12, 2011"
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==Solution== | ==Solution== | ||
− | {{ | + | Let's take a look at the units digit of <math>39</math>, which is <math>9</math>. Now, let's take a look at the positive numbers that add up to to <math>9</math>: |
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+ | <cmath>1,8</cmath> | ||
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+ | <cmath>2,7</cmath> | ||
+ | |||
+ | <cmath>3,6</cmath> | ||
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+ | <cmath>4,5</cmath> | ||
+ | |||
+ | Now, we realize that every pair has an even element. Any number with an even units digit is even. So, what is the only even prime? <math>2</math>! So, one of our primes is <math>2</math>. The other is then, consequently, <math>37</math>. The product is then: | ||
+ | |||
+ | <cmath>2\cdot{37}=\boxed{74}</cmath> |
Latest revision as of 17:40, 11 June 2011
Problem
AoPSWiki:Problem of the Day/June 12, 2011
Solution
Let's take a look at the units digit of , which is . Now, let's take a look at the positive numbers that add up to to :
Now, we realize that every pair has an even element. Any number with an even units digit is even. So, what is the only even prime? ! So, one of our primes is . The other is then, consequently, . The product is then: