Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 315. (December 2011)

K. 315. Let \downarrow\! n\! \downarrow denote the greatest prime number smaller than n, and let \uparrow\! n\! \uparrow denote the smallest prime greater than n. Calculate the value of the expression 41+ \downarrow\! 35\!
\downarrow - \uparrow\! 53\! \uparrow + \big\uparrow\! \downarrow\! 40\!
\downarrow\! \big\uparrow.

(6 pont)

Deadline expired on January 10, 2012.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás. \(\displaystyle \downarrow\! 35\! \downarrow=31\), \(\displaystyle \uparrow\! 53\! \uparrow =59\), \(\displaystyle \uparrow\downarrow\! 40\! \downarrow\uparrow=\uparrow\! 37\! \uparrow=41\), tehát a keresett kifejezés értéke \(\displaystyle 41+31–59+41=54\).


Statistics:

278 students sent a solution.
6 points:58 students.
5 points:85 students.
4 points:93 students.
3 points:24 students.
2 points:9 students.
1 point:2 students.
0 point:1 student.
Unfair, not evaluated:6 solutions.

Problems in Mathematics of KöMaL, December 2011