  Discoveries from the prime Kepler mission demonstrated that small planets (<
3 Earth-radii) are common outcomes of planet formation. While Kepler detected
many such planets, all but a handful orbit faint, distant stars and are not
amenable to precise follow up measurements. Here, we report the discovery of
two small planets transiting K2-21, a bright (K = 9.4) M0 dwarf located
65$\pm$6 pc from Earth. We detected the transiting planets in photometry
collected during Campaign 3 of NASA's K2 mission. Analysis of transit light
curves reveals that the planets have small radii compared to their host star,
2.60 $\pm$ 0.14% and 3.15 $\pm$ 0.20%, respectively. We obtained follow up NIR
spectroscopy of K2-21 to constrain host star properties, which imply planet
sizes of 1.59 $\pm$ 0.43 Earth-radii and 1.92 $\pm$ 0.53 Earth-radii,
respectively, straddling the boundary between high-density, rocky planets and
low-density planets with thick gaseous envelopes. The planets have orbital
periods of 9.32414 days and 15.50120 days, respectively, and have a period
ratio of 1.6624, very near to the 5:3 mean motion resonance, which may be a
record of the system's formation history. Transit timing variations (TTVs) due
to gravitational interactions between the planets may be detectable using
ground-based telescopes. Finally, this system offers a convenient laboratory
for studying the bulk composition and atmospheric properties of small planets
with low equilibrium temperatures.
